Two similar right triangles have areas of 6 square inches and

Question

directrix · Answer

and ...?

anonymous · Answer

150 square inches. The length of the hypotenuse of the smaller
triangle is 5 inches. What is the sum of the lengths of the legs
of the larger triangle?

directrix · Answer

The ratio of the corresponding area from small to large = 6/150 = 1/25.

For similar triangles, the square of the scale factor is the ratio of corresponding linear parts of the 2 trianlges. So the scale factor is 1 to 5  or 1/5.  and....

directrix · Answer

1/5 = 5/h where h is the hypotenuse of the larger triangle.

h = 25.

directrix · Answer

The perimeters are also in the ratio 1/5 -- same as scale factor.

directrix · Answer

What is the sum of the lengths of the legs
of the larger triangle?

If the sides of the larger triangle form a Pythagorean triple, then that triple is (9, 12, 15) which is a multiple of (3,45). 9+12+15 = 36 - 15 = 21 for sum of legs.