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First we need to calculate the area of triangle ABD so we can find the area of triangle ADC. ABD area = 8 x 6/2 ABD area - 24 m^2
ABC area is 50% more, meaning 24 + (24/2) = 24 + 12 = 36m^2.
Also we know that the area of ADC is (b x h)/2. This is equal to (DC)(8)/2 which is equal to 4DC. Since we have the area, we can plug it in. 36 = 4(DC). DC = 9m.
Using the 3-4-5 Pythagorean triple, we know that the base to multiply triangle ABD by is 2. 3 x 2 = 6, 4 x 2 = 8, so 5 x 2 = 10. Side length AD is 10m.
Since we have BD and DC, we can add them together (6+9 = 15) to get length BC. This will allow us to find length AC. There is one length of 8, one of 15 and one missing length. Using the triple 8-15-17, we know that length AC is 17m.
Now we can find the perimeter of triangle ADC. 10+9+17 = 27+9 = 36
Hi. I forgot this site existed... ;-; This one is simple. I first used the theorem to find the length of AD, which was 10 (8*8=64, 6*6=36, 64+36=100) Then, I calculated the length of DC. Because the triangle ADC is 50% longer than the triangle ABD, I can see that the line DC is also 50% longer than the line BD. That meant that the line DC was equal to 9. Then, I used the theorem to find the length of AC, using the triangle ABC, which added up to the square root of 289, which turned out to be 17. Finally, I added the values (10, 9, 17) and I got a perimeter of 36.
Grade 7/8 POTW First, let’s list the facts: - Angle ABC is 90 degrees - Line segment BD is 6 m - Line segment AB is 8 m - The area of triangle ADC is 50% more than the area of triangle ABD We know that since angle ABC is 90 degrees, Triangle ABD and ABC are right triangles. This means that their hypotenuse squared is equal to the sum of the other two side lengths squared due to the pythagorean theorem. Since AB is 8m, and BD is 6 m: a^2 + b^2 = c^2 8^2 + 6^2 = (AD)^2 64 + 36 = (AD)^2 100 = (AD)^2 10 m = Line Segment AD Now let’s find the area of both triangle ABD and triangle ACD. The area of a triangle is (b x h)/2 so: (bh)/2 = (Triangle ABD Area) (6 x 8)/2 = (Triangle ABD Area) (48)/2 = (Triangle ABD Area) 24 m^2 = Triangle ABD Area Since triangle ACD has a 50% larger area: 24 + 24(0.5) = 24 x 1.5 = 36 m^2 = Triangle ACD Area We can now find the length of CD using the area of a triangle ((b x h)/2) as we have the height value (8 m) and the area (36 m^2): (bh)/2 = Triangle ACD Area ((CD)(8))/2 = 36 (CD)(8) = 72 CD = 9 m Now we can find the length of line segment AC using the pythagorean theorem again: a^2 + b^2 = c^2 8^2 + (6 + 9)^2 = (AC)^2 64 + 15^2 = (AC)^2 64 + 225 = (AC)^2 289 = (AC)^2 17 m = Line Segment AC We can now find the perimeter of triangle ADC using addition: (AC) + (AD) + (CD) = Perimeter of Triangle ADC 17 + 10 + 9 = Perimeter of Triangle ADC 36 m = Perimeter of Triangle ADC Therefore, the perimeter of Triangle ADC is 36m.
Grade 7/8 POTW:
ReplyDeleteFirst we need to calculate the area of triangle ABD so we can find the area of triangle ADC.
ABD area = 8 x 6/2
ABD area - 24 m^2
ABC area is 50% more, meaning 24 + (24/2) = 24 + 12 = 36m^2.
Also we know that the area of ADC is (b x h)/2. This is equal to (DC)(8)/2 which is equal to 4DC. Since we have the area, we can plug it in. 36 = 4(DC). DC = 9m.
Using the 3-4-5 Pythagorean triple, we know that the base to multiply triangle ABD by is 2. 3 x 2 = 6, 4 x 2 = 8, so 5 x 2 = 10. Side length AD is 10m.
Since we have BD and DC, we can add them together (6+9 = 15) to get length BC. This will allow us to find length AC. There is one length of 8, one of 15 and one missing length. Using the triple 8-15-17, we know that length AC is 17m.
Now we can find the perimeter of triangle ADC. 10+9+17 = 27+9 = 36
The perimeter of triangle ADC is 36m.
Hi. I forgot this site existed... ;-;
ReplyDeleteThis one is simple.
I first used the theorem to find the length of AD, which was 10 (8*8=64, 6*6=36, 64+36=100)
Then, I calculated the length of DC. Because the triangle ADC is 50% longer than the triangle ABD, I can see that the line DC is also 50% longer than the line BD. That meant that the line DC was equal to 9. Then, I used the theorem to find the length of AC, using the triangle ABC, which added up to the square root of 289, which turned out to be 17. Finally, I added the values (10, 9, 17) and I got a perimeter of 36.
POTW:
ReplyDeleteMy POTW was done on paper, answer: perimeter of triangle ADC is 36 m.
Grade 7/8 POTW
ReplyDeleteFirst, let’s list the facts:
- Angle ABC is 90 degrees
- Line segment BD is 6 m
- Line segment AB is 8 m
- The area of triangle ADC is 50% more than the area of triangle ABD
We know that since angle ABC is 90 degrees, Triangle ABD and ABC are right triangles. This means that their hypotenuse squared is equal to the sum of the other two side lengths squared due to the pythagorean theorem. Since AB is 8m, and BD is 6 m:
a^2 + b^2 = c^2
8^2 + 6^2 = (AD)^2
64 + 36 = (AD)^2
100 = (AD)^2
10 m = Line Segment AD
Now let’s find the area of both triangle ABD and triangle ACD. The area of a triangle is (b x h)/2 so:
(bh)/2 = (Triangle ABD Area)
(6 x 8)/2 = (Triangle ABD Area)
(48)/2 = (Triangle ABD Area)
24 m^2 = Triangle ABD Area
Since triangle ACD has a 50% larger area:
24 + 24(0.5) = 24 x 1.5 = 36 m^2 = Triangle ACD Area
We can now find the length of CD using the area of a triangle ((b x h)/2) as we have the height value (8 m) and the area (36 m^2):
(bh)/2 = Triangle ACD Area
((CD)(8))/2 = 36
(CD)(8) = 72
CD = 9 m
Now we can find the length of line segment AC using the pythagorean theorem again:
a^2 + b^2 = c^2
8^2 + (6 + 9)^2 = (AC)^2
64 + 15^2 = (AC)^2
64 + 225 = (AC)^2
289 = (AC)^2
17 m = Line Segment AC
We can now find the perimeter of triangle ADC using addition:
(AC) + (AD) + (CD) = Perimeter of Triangle ADC
17 + 10 + 9 = Perimeter of Triangle ADC
36 m = Perimeter of Triangle ADC
Therefore, the perimeter of Triangle ADC is 36m.