SOLUTION: The perimeters of two similar triangles is in the ratio 3:4. The sum of their area is 75cm^2. Find the area of each triangle.

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Question 1015241: The perimeters of two similar triangles is in the ratio 3:4. The sum of their area is 75cm^2. Find the area of each triangle.
Answer by ikleyn(52754) About Me  (Show Source):
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The perimeters of two similar triangles is in the ratio 3:4. The sum of their area is 75cm^2. Find the area of each triangle.
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If the perimeters' ratio is 3:4, then the areas' ratio is 9:16 (the triangles are similar !).


Since S1 + S2 = 75 cm%5E2 and S1%2FS2 = 9%2F16, then

S1 = 75%2A%289%2F%289%2B16%29%29 = %2875%2A9%29%2F25 = 3*9 = 27 cm%5E2 and 

S2 = 75%2A%2816%2F%289%2B16%29%29 = %2875%2A16%29%2F25 = 3*16 = 48 cm%5E2.