SOLUTION: pls. help me to answer: Two similar triangles have perimeters 100 cm and 75 cm. if the area of the smaller triangle is 20 sq.cm. find the area of the larger triangle.

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Question 1096213: pls. help me to answer: Two similar triangles have perimeters 100 cm and 75 cm. if the area of the smaller triangle is 20 sq.cm. find the area of the larger triangle.
Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe the ratio of the sides will be 100/75 = 4/3.

the ratio of the area should therefore be 4^2 / 3^2 = 16/9.

if that's true, then the area of the larger triangle should be 20 * 16 / 9 = 35.56 rounded to 2 decimal places.

i checked the web and found it to be true.

here's a reference.

https://www.cliffsnotes.com/study-guides/geometry/similarity/similar-triangles-perimeters-and-areas

i checked this out with an example and it is proven to be correct.

if the ratio of the perimeter is 4/3, then the ratio of the area is (4/3)^2 = 16/9.





Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
system%282x%2B2y=75%2C2kx%2B2ky=100%2C%281%2F2%29xy=20%2C%281%2F2%29xyk%5E2%29

system%28x%2By=37%261%2F2%2Ck%28x%2By%29=50%29

k=50%2F%2837%261%2F2%29

highlight_green%28k=4%2F3%29

Area of the larger triangle: highlight_green%2820%2Ak%5E2%29=20%284%2F3%29%5E2=320%2F9=highlight%2835%265%2F9%29