SOLUTION: The ratio of the areas of two similar triangles is 4:5. If the legs of the smaller triangle are 3cm and 4cm, how long is the hypotenuse of the larger triangle?

Question 465192: The ratio of the areas of two similar triangles is 4:5. If the legs of the smaller triangle are 3cm and 4cm, how long is the hypotenuse of the larger triangle?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The hypotenuse of the smaller triangle is 5.

To find the hypotenuse of the larger triangle, note that the areas are in the ratio 4:5, with 4 corresponding to the smaller triangle. This is a two dimensional specification, so if we take the square root we will obtain the ratio of side lengths (one dimensional).

The ratio of the side lengths of the two triangles is 2:sqrt(5). Here we can build a ratio:

Solving, we get

.
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