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The method is simple once you know the method. This method is called Pythagorean Theorem. The method includes two legs, 1 hypotenuse and of course a right triangle,
The legs mean the sides that make the 90 degree angle. (PQ, PU,RT and TS) The hypotenuse is the opposite side of the 90 degree angle. The sides are. PQ, RS and QR (il tell later why QR is a side)
So what you do with the legs first is to find the square root of the sides. We do the triangle on the right first. 3²= 9 4²=16 Add them both together and you get 25. Soon you have to find the √ √25=5 5 is how much PQ represents
Second triangle on the right. Same method, find the legs and put them into square root 4²=16 7.5²=56.25 Add them together you get 72.25 √72.25=8.5 RS= 8.5
Now to show the last triangle. Take out the triangles that you already used and you get a weird shape. At the top, that is where your triangle is. So imagine a line through the point Q and to the 7.5 line. We dont know all the sides measurements so what I did is 7.5 - 4 = 3.5. The reason I did that is because to know the extra side at the base of the triangle
Our new measurements are Legs= 3.5 and 12. (12 because the bottom of the whole shape is the same sides as the line)
3.5²=12.25 12²= 144 Add them together to make 156.25 √156.25 = 12.5 12.5= QR
Now to add the sides together to calculate the tarp.
12.5 + 5 + 8.5 = 26
So, My final answer is that the whole tarp is 26 meters long That is all Byeeeee!! lads
The answer we got was 25.75m as the total length of the tarp.
We used the formula of finding the side lengths of a right triangle, also known as the pythagorean theorem. *this only works when two of the side lengths are already given
We used this formula to find the length of PQ, QR and RS.
As seen above, triangles were already outlined (triangle QPU, triangle RTS).
(formula : a² + b² = c²) "c" is the hypotenuse, the longest side of a triangle. "a" and "b" are the two other sides
Triangle QRV (since there was not a length given, we decided to draw a straight line starting at Q, this resulted in a right triangle) : *side QV is the length of 12m RV is the length of 3.5m (7.5 - 4)
12² + 3.5² = QR² 144 + 12.25 = QR² 156.25 = QR² QR² = 156.25 QR = √156.25 QR = 12.25 m
Wow good job all of you! I'm impressed. John, you were exactly right in knowing that the Pythagorean theorem would need to be used. The answer for the tarp's length is 26m. Jonathan and Rachel, you basically got the exact same answer! Good job! Do you see where the 0.25m comes from to give you 26m, instead of 25.75m?
Yello mates,
ReplyDeleteThe method is simple once you know the method.
This method is called Pythagorean Theorem. The method includes two legs, 1 hypotenuse and of course a right triangle,
The legs mean the sides that make the 90 degree angle. (PQ, PU,RT and TS)
The hypotenuse is the opposite side of the 90 degree angle. The sides are. PQ, RS and QR (il tell later why QR is a side)
So what you do with the legs first is to find the square root of the sides.
We do the triangle on the right first.
3²= 9
4²=16
Add them both together and you get 25. Soon you have to find the √
√25=5
5 is how much PQ represents
Second triangle on the right.
Same method, find the legs and put them into square root
4²=16
7.5²=56.25
Add them together you get 72.25
√72.25=8.5
RS= 8.5
Now to show the last triangle.
Take out the triangles that you already used and you get a weird shape. At the top, that is where your triangle is. So imagine a line through the point Q and to the 7.5 line. We dont know all the sides measurements so what I did is 7.5 - 4 = 3.5. The reason I did that is because to know the extra side at the base of the triangle
Our new measurements are
Legs= 3.5 and 12. (12 because the bottom of the whole shape is the same sides as the line)
3.5²=12.25
12²= 144
Add them together to make 156.25
√156.25 = 12.5
12.5= QR
Now to add the sides together to calculate the tarp.
12.5 + 5 + 8.5 = 26
So, My final answer is that the whole tarp is 26 meters long
That is all
Byeeeee!! lads
You continue to show all your work so your work is very clear.
DeleteI like how you explained the answer in full detail so that viewers could understand your step through step process. Keep up the good work!
DeleteHello.
ReplyDeleteThe answer we got was 25.75m as the total length of the tarp.
We used the formula of finding the side lengths of a right triangle, also known as the pythagorean theorem.
*this only works when two of the side lengths are already given
We used this formula to find the length of PQ, QR and RS.
As seen above, triangles were already outlined (triangle QPU, triangle RTS).
(formula : a² + b² = c²)
"c" is the hypotenuse, the longest side of a triangle.
"a" and "b" are the two other sides
Triangle QPU:
3² + 4² = PQ²
9 + 16 = PQ²
25 = PQ²
PQ² = 25
PQ = √25
PQ = 5m
Triangle QRV (since there was not a length given, we decided to draw a straight line starting at Q, this resulted in a right triangle) :
*side QV is the length of 12m
RV is the length of 3.5m (7.5 - 4)
12² + 3.5² = QR²
144 + 12.25 = QR²
156.25 = QR²
QR² = 156.25
QR = √156.25
QR = 12.25 m
Triangle RTS:
4² + 7.5² = RS²
16 + 56.25 = RS²
72.25 = RS²
RS² = 72.25
RS = √72.25
RS = 8.5m
5 + 12.25 + 8.5 = 25.75m
- Rachel and Jonathan
Wow good job all of you! I'm impressed. John, you were exactly right in knowing that the Pythagorean theorem would need to be used. The answer for the tarp's length is 26m. Jonathan and Rachel, you basically got the exact same answer! Good job! Do you see where the 0.25m comes from to give you 26m, instead of 25.75m?
ReplyDeletePQ=5m QR= 12.5 RS=8.5 5+12.5+8.5=26
ReplyDelete