Question

The sides of a triangle are 3, 7, and 9. Find the length of the longest side of a similar triangle whose shortest side is 4.

Highschool geometry

Answer 1

The longest side of the new triangle is 12.

Explanation:

Drawing a picture can help! One triangle is given, the 3, 7, 9 triangle.

The other triangle is similar (same shape but different size)

The 3 in the original triangle "grows" to 4 in the new triangle. So they are asking what does the 9 "grow" to in the new triangle?

see image.

Since the triangles are similar, the ratios of the sides must be the same. So you can set up a proportion (two ratios equal to each other) and solve. See image.

There are two great ways to set up the proportion, just do the same set up on both sides of the equal sign. See image.