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POTW 7/8 Instead of listing the facts for this one, I’ll go straight into the math because it is kind of stated what to do already. Also, everything here is needed. The most important thing I need to keep in mind is the pythagoras theorem, a^2 + b^2 = c^2. This’ll find out the length of c which is the value depending on which triangle I take. First, I’ll calculate PQ. 3^2 + 4^2 = 25 = 5^2 PQ = 5 m Next, I’ll calculate RS. 4^2 + 7.5^2 = 72.25 = 8.5^2 RS = 8.5 m FInally, I’ll calculate QR. Before do that, I need to calculate side lengths a and b to get c. Line UT going parallel to a new line starting at angle RQU, but still having 12 m, but going left will make another line that would be a/b (doesn’t matter. The second line would be part of line RT, 4 m less specifically due to the line a/b being moved 4 m up. 7.5 - 4 = 3.5 Finally, I’ll actually calculate QR. 12^2 + 3.5^2 = 156.25 = 12.5 QR = 12.5 I’ll restate the values of PQ, QR and RS. PQ = 5 m QR = 12.5 m RS = 8.5 m 5 + 12.5 + 8.5 = 26 PQ + QR + RS = 26 m (I might reply to this comment if I made a small error)
For sides PQ and RS, we can use the pythagorean theorem (a^2 + b^2 = c^2) to find their lengths. PQ: 3^2 = 9 4^2 = 16 16 + 9 = 25 √25 = 5 Therefore, line PQ equals 5 m.
To calculate QR, we need to get rid of the quadrilateral (not actually) and make it a triangle. That is why we subtract 4 from 7.5 to give us 3.5. Now the pythagorean theorem can be used again. 12^2 = 144 3.5^2 = 12.25 144 + 12.25 = 156.25 √156.25 = 12.5 Therefore, line QR equals 12.5 m.
Now we just add up the values and get our answer. 5 + 8.5 + 12.5 = 26
7/8 POTW: For POTW, I need to use the pythagorean theorem ("A squared plus B sqaured is C sqaured" or "length(squared) plus width(squared) is the hypotenuse (squared)"). Info: - QU- 4 m - RT- 7.5 m - PU- 3 m - TS- 4 m Need to find: PQ+QR+RS
First off, I need to find out what PQ is. The length 4 and the width is 3, so the equation must be 16 (4 squared)+ 9 (3 squared)=25. And since 25 is 5 squared, PQ must be 5. Next, I need to figure out QR. To do this, I must make the quadrilateral a triangle. I can do this by making a sline parrallel to line UT. To fidn the lenght, I can take 12 as the length has not gotten shorter or longer. For the width, I would need to subtract 4 (Line QU) from 7.5. The width is 3.5. To calculate: 12 squared+3.5 squared= 156.25. 156.25's square root is 12.5. QR= 12.5 RS= 7.5 (squared)+4 (squared)= 8.5 (squared)
For this question, we are going need to use the Pythagorean theorem (a^2 + b^2 = c^2)
Let's start off with PQ...
3^2 = 9 and 4^2 = 16 9+16 = 25
To find PQ^2, since its squared we need to find the square root of 25, which is 5 Therefore PQ = 5
Let's try it with RS...
7.5 ^2 = 56.25 and 4^2 = 16 56.25 + 16 = 76.25
Again, we need to find the square root of 76.25 which is 8.5 For QR, we need to take away 4 from 7.5, so it will "fit" into the Pythagorean theorem. Now we can continue...
12^2 =144 and 3.5^2 = 12.25 144 + 12.25 = 156.25
The square root of 156.25 is 12.5. All we do now is add the amounts together to get the tarp length...
And its back to another week of POTW: I don't really need to explain much for this problem. All I have to do is to follow the Pythagorean theorem. For length PQ, I don't even have to calculate it because I have it memorized. The diagonal will always be 5. For length QR, I use the heights and subtract them to get the difference, which is 3.5. This would allow me to get the other side to figure out the diagonal. Now I have 3.5, 12, and this is enough for me to figure out the diagonal QR, which is 12.5. The other side length would be 8.5, since I use the theorem on the two sides, 4 and 7.5. Adding these together, I get 26 meters. -Alan
POTW #13 After figuring out what the Pythagorean theorum was and what it was figuring out, I now know that I am finding: a^2 + b^2 = c^2 To start with PQ: 3 x 3 = 9 4 x 4 = 16 9 + 16 = 25 but since 25 is c^2 I need to find the square root, which is 5. Then I do the same with RS: 7.5 x 7.5 = 56.25 4 x 4 = 16 56.25 + 16 = 76.25 and the square root is 8.5 QR: 7.5 - 4 = 3.5 3.5 x 3.5 = 12.25 12 x 12 = 144 12.25 + 144 = 156.25 which as the square root of 12.5
Then, we do: PQ + QR + RS = 5 + 8.5 + 12.5 Which is 26. Therefore the length of the tarp is 26m.
QR : I needed to change this weird polygon so I did 7.5 - 4 = 3.5 which is my new side length = 3.5^ + 12^ = 12.25 + 144 = 156.25 square root of 156.25 is 12.5 QR = 12.5
RS = 4^ + 7.5^ = 56.25 + 16 = 72.25 square root of 72.25 is 8.5
POTW #13: I used the Pythagorean theorem for this, and I did it on paper. Essentially, since I know a2 + b2 = c2 I can use that. For triangle PQU, I saw the numbers 3 and 4 for sides A and B. So using background knowledge, I know the smallest triangle sides is 3, 4 and 5 so I know that side is 5m. So we do that for RST, and we get 8.5m. To find QR, I just moved the bottom up, so it formed a triangle instead of a quadrilateral. So 7.5-4= 3.5. So one of the sides was 3.5, and the other was 12. And if we do the math, we get 12.5 as the hypotenuse.
UT = 12m Height = 3.5m Height is 3.5m as 7.5m - 4m = 3.5m (Use same formula A squared plus B squared = C squared) UT squared = 12*12 = 144m squared 3.5 squared = 12.25m squared 144+12.25 = 156.25m squared UT = square root of 156.25 = 12.5m
To solve the question, I drew out the figure than measured the sides. After finding that PQ is 5,QR is 12.5, and RS is 8.5, I totaled the numbers up to 26. For those reasons I believe the tarp is 26m long. All work done on paper.
POTW 7/8
ReplyDeleteInstead of listing the facts for this one, I’ll go straight into the math because it is kind of stated what to do already. Also, everything here is needed. The most important thing I need to keep in mind is the pythagoras theorem, a^2 + b^2 = c^2. This’ll find out the length of c which is the value depending on which triangle I take.
First, I’ll calculate PQ.
3^2 + 4^2 = 25 = 5^2
PQ = 5 m
Next, I’ll calculate RS.
4^2 + 7.5^2 = 72.25 = 8.5^2
RS = 8.5 m
FInally, I’ll calculate QR. Before do that, I need to calculate side lengths a and b to get c. Line UT going parallel to a new line starting at angle RQU, but still having 12 m, but going left will make another line that would be a/b (doesn’t matter. The second line would be part of line RT, 4 m less specifically due to the line a/b being moved 4 m up.
7.5 - 4 = 3.5
Finally, I’ll actually calculate QR.
12^2 + 3.5^2 = 156.25 = 12.5
QR = 12.5
I’ll restate the values of PQ, QR and RS.
PQ = 5 m
QR = 12.5 m
RS = 8.5 m
5 + 12.5 + 8.5 = 26
PQ + QR + RS = 26 m
(I might reply to this comment if I made a small error)
For sides PQ and RS, we can use the pythagorean theorem (a^2 + b^2 = c^2) to find their lengths.
ReplyDeletePQ:
3^2 = 9
4^2 = 16
16 + 9 = 25
√25 = 5
Therefore, line PQ equals 5 m.
RS:
7.5^2 = 56.25
4^2 = 16
56.25 + 16 = 72.25
√72.25 = 8.5
Therefore, line RS equals 8.5 m.
To calculate QR, we need to get rid of the quadrilateral (not actually) and make it a triangle. That is why we subtract 4 from 7.5 to give us 3.5. Now the pythagorean theorem can be used again.
12^2 = 144
3.5^2 = 12.25
144 + 12.25 = 156.25
√156.25 = 12.5
Therefore, line QR equals 12.5 m.
Now we just add up the values and get our answer.
5 + 8.5 + 12.5 = 26
Therefore, the length of the tarp is 26 m.
PQ:
ReplyDelete3^2 + 4^2 = PQ^2
9 + 16 = PQ^2
25 = PQ^2
5 = PQ
RS:
56.25 + 16 = RS^2
76.25 = RS^2
8.5 = RS
QR
7.5 - 4 = 3.5
12^2 + 3.5^2 = QR^2
144 + 12.25 = QR^2
156.25 = QR^2
12.5 = QR
12.5 + 8.5 + 5
= 26
The tarp length is 26 m.
Your answer seems to be correct but you made a calculation error in the middle. You wrote:
Delete56.25 + 16 = RS^2
76.25 = RS^2
56.25 + 16 does not equal 76.25 but 72.25.
Great eye Avi!
Deletea^2 + b^2 = c^
ReplyDeletePQ:
3^2 + 4^2 = c^2
9 + 16 = c^2
c = square root of 25
c = 5
PQ = 5
RS:
7.5^2 + 4^2 = c^2
56.25 + 16 = c^2
72.25 = c^2
c = square root of 72.25
c = 8
RS = 8
QR:
7.5 - 4 = 3.5
12^2 + 3.5^2 = c^2
144 + 12.25 = c^2
156.25 = c^2
c = square root of 156.25
c = 12.5
QR = 12.5
12.5 + 8.5 + 5
= 26
The length of the tarp is 26
26 what? Sticks? Pencil lengths? kilometres?
DeleteI think you made an error for the square root of 72.25.
DeleteThat was a typo. I meant to write 8.5 not 8.
DeleteThe length of the tarp is 26m.
7/8 POTW:
ReplyDeleteFor POTW, I need to use the pythagorean theorem ("A squared plus B sqaured is C sqaured" or "length(squared) plus width(squared) is the hypotenuse (squared)").
Info:
- QU- 4 m
- RT- 7.5 m
- PU- 3 m
- TS- 4 m
Need to find:
PQ+QR+RS
First off, I need to find out what PQ is. The length 4 and the width is 3, so the equation must be 16 (4 squared)+ 9 (3 squared)=25. And since 25 is 5 squared, PQ must be 5.
Next, I need to figure out QR. To do this, I must make the quadrilateral a triangle. I can do this by making a sline parrallel to line UT. To fidn the lenght, I can take 12 as the length has not gotten shorter or longer. For the width, I would need to subtract 4 (Line QU) from 7.5. The width is 3.5. To calculate: 12 squared+3.5 squared= 156.25. 156.25's square root is 12.5.
QR= 12.5
RS= 7.5 (squared)+4 (squared)= 8.5 (squared)
8.5+12.5+5= 26.
The tarp's length is 26.
POTW:
ReplyDeleteFor this question, we are going need to use the Pythagorean theorem (a^2 + b^2 = c^2)
Let's start off with PQ...
3^2 = 9 and 4^2 = 16
9+16 = 25
To find PQ^2, since its squared we need to find the square root of 25, which is 5
Therefore PQ = 5
Let's try it with RS...
7.5 ^2 = 56.25 and 4^2 = 16
56.25 + 16 = 76.25
Again, we need to find the square root of 76.25 which is 8.5
For QR, we need to take away 4 from 7.5, so it will "fit" into the Pythagorean theorem. Now we can continue...
12^2 =144 and 3.5^2 = 12.25
144 + 12.25 = 156.25
The square root of 156.25 is 12.5.
All we do now is add the amounts together to get the tarp length...
5 + 8.5 + 12.5 = 26
Therefore, the length of the tarp is 26 m.
And its back to another week of POTW:
ReplyDeleteI don't really need to explain much for this problem. All I have to do is to follow the Pythagorean theorem. For length PQ, I don't even have to calculate it because I have it memorized. The diagonal will always be 5.
For length QR, I use the heights and subtract them to get the difference, which is 3.5. This would allow me to get the other side to figure out the diagonal. Now I have 3.5, 12, and this is enough for me to figure out the diagonal QR, which is 12.5. The other side length would be 8.5, since I use the theorem on the two sides, 4 and 7.5. Adding these together, I get 26 meters.
-Alan
Grade 8 POTW:
ReplyDeleteI used the Pythagorean theorem to figure out the lengths of the following lengths. The total meters of PQ, QR and RS is 26. I did my work on paper.
POTW #13
ReplyDeleteAfter figuring out what the Pythagorean theorum was and what it was figuring out, I now know that I am finding:
a^2 + b^2 = c^2
To start with PQ:
3 x 3 = 9
4 x 4 = 16
9 + 16 = 25 but since 25 is c^2 I need to find the square root, which is 5.
Then I do the same with RS:
7.5 x 7.5 = 56.25
4 x 4 = 16
56.25 + 16 = 76.25 and the square root is 8.5
QR:
7.5 - 4 = 3.5
3.5 x 3.5 = 12.25
12 x 12 = 144
12.25 + 144 = 156.25 which as the square root of 12.5
Then, we do: PQ + QR + RS = 5 + 8.5 + 12.5
Which is 26. Therefore the length of the tarp is 26m.
For this you would have to use Pythagorean theorem, so here I go....
ReplyDeletePQ = 3^ + 4^
= 9 + 16
= 25
= square root of 25 = 5
PQ = 5
QR : I needed to change this weird polygon so I did 7.5 - 4 = 3.5 which is my new side length
= 3.5^ + 12^
= 12.25 + 144
= 156.25
square root of 156.25 is 12.5
QR = 12.5
RS = 4^ + 7.5^
= 56.25 + 16
= 72.25
square root of 72.25 is 8.5
all them all up I get 26
5 + 12.5 + 8.5
POTW #13:
ReplyDeleteI used the Pythagorean theorem for this, and I did it on paper. Essentially, since I know a2 + b2 = c2
I can use that. For triangle PQU, I saw the numbers 3 and 4 for sides A and B. So using background knowledge, I know the smallest triangle sides is 3, 4 and 5 so I know that side is 5m. So we do that for RST, and we get 8.5m. To find QR, I just moved the bottom up, so it formed a triangle instead of a quadrilateral. So 7.5-4= 3.5. So one of the sides was 3.5, and the other was 12. And if we do the math, we get 12.5 as the hypotenuse.
12.5+8.5+5
=21+5
=26m
The perimeter/length of the tarp is 26m.
Grade 8 POTW
ReplyDeletePQ is 5 metres long, RS is 8.5 metres long, and QR is 12.5 metres long. Therefore, the length of the tarp is 26 m. I did my work on paper
Pythagoras Theorem:
ReplyDeletePU = 3m
Height = 4m
PU squared + Height Squared = PQ squared
PU = 9m squared
Height = 16m squared
9+16 = 25m squared
PQ squared = 25m
PQ = 5m
UT = 12m
Height = 3.5m
Height is 3.5m as 7.5m - 4m = 3.5m
(Use same formula A squared plus B squared = C squared)
UT squared = 12*12 = 144m squared
3.5 squared = 12.25m squared
144+12.25 = 156.25m squared
UT = square root of 156.25 = 12.5m
TS = 4m
Height = 7.5m
(Same formula as before)
TS squared = 4*4 = 16m squared
Height squared = 7.5*7.5 = 56.25m squared
16+56.25 = 72.25m squared
RS = square root of 72.25 = 8.5m
PQ (5m) + QR (12.5m) + RS (8.5m) = 26m
Therefore the length of the tarp is 26m
POTW #13:
ReplyDeleteOkie. The Pythagorean theorem is needed to find the solution.
Pythagorean Theorem: A2 + B2 = C2
We can find the lines RS and PQ since the measurements needed to use the Pythagorean Theorem are already there.
RS:
A = 7.5 (squared)= 56.25m
B = 4 (squared) = 16m
A (squared) + B (squared) = C (squared)/72.25m (squared)
RS = 8.5m
PQ:
A = 4 (squared) = 16m
B = 3 (squared) = 9m
A (squared) + B (squared) = C (squared)/25m (squared)
PQ = 5m
Now for QR, we'll just have to subtract 7.5 - 4 to make the shape a triangle in order for the Pythagorean theorem to work.
QR:
A = 3.5 (squared) = 12.25m
B = 12 (squared) = 144m
A (squared) + B (squared) = C (squared)/156.25m (squared)
QR = 12.5m
8.5 + 5 + 12.5 = 26m
The length of the tarp is 26m.
The tarp has a length of 26 meters as proven by the Pythagorean theorem.
ReplyDeleteI got 26m for the length of the tarp. Work on paper.
ReplyDeleteTo solve the question, I drew out the figure than measured the sides. After finding that PQ is 5,QR is 12.5, and RS is 8.5, I totaled the numbers up to 26. For those reasons I believe the tarp is 26m long.
ReplyDeleteAll work done on paper.
POTW #13:
ReplyDeleteTo solve the question, I used the Pythagorean Theorem.
Equation: a^2 + b^2 = c^2
PQ = 5m QR = 8.5m RS = 12.5m
Total: 5 + 8.5 + 12.5 = 26
Therefore, the length of the tarp is 26m.