SOLUTION: The perimeter of two similar triangles have a ratio of 2:4. The sum of the areas of the triangles add up to 100cm^2. What is the area of each triangle?

Question 855643: The perimeter of two similar triangles have a ratio of 2:4. The sum of the areas of the triangles add up to 100cm^2. What is the area of each triangle?
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Perimeter being a length, or a distance, means the side lengths are also in the same 2:4 proportion, actually 1:2 ratio, because 1:2 is reduced.

Small triangle:
perimeter x+y+z, and if assumed z is a hypotenuse and the triangles are Right, then
area is .

Large triangle:
perimeter would be 2x+2y+2z=2(x+y+z). As similar to the small one,
area is .

Look at now the ratio of their areas. (1/2):2, or , small to large; This means, if cut the large AND small together into 5 equal parts, the small triangle is 1 of those parts, and the large triangle is 4 of those parts; together making the 5 equal parts.

Cut into 5 equal parts: in each part. This means small triangle is and large triangle is .
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