two right triangles are similar.. (see below for more)

Question

5→📐 3.8→📐 (imagine this one is smaller)

↑ ↑

12 9

I solved the majority of the problem however I'm a bit stuck on how to find the hypotenuse of the "smaller" triangle.

would I use the Pythagorean theorem (3.82 +92=c2) or do I determine the hypotenuse of the larger triangle and then use the unit rate (12/9) of that triangle to solve the problem, if so do I multiply the rate by the larger triangles hypotheses or divide it?

Answer 1

By the Pythagorean theorem, the hypotenuse of the larger triangle is 13.

Let x = length of hypotenuse of the other triangle.

Since the triangles are similar, we have: 9/12 = x/13

So, 12x = 117

x = 117/12 = 39/4 = 12.75