Question

Triangle A has sides of lengths `18`, `12`, and `12`. Triangle B is similar to triangle A and has a side of length `24`. What are the possible lengths of the other two sides of triangle B?

Answer 1

See explanation.

Explanation:

There are 2 possible solutions:

Both triangles are isosceles.

Solution 1

The base of the larger triangle is `24` units long.
The scale of similarity would then be: `k=24/18=4/3`.
If the scale is `k=4/3`, then the equal sides would be `4/3*12=16` units long.

This means that the triangle's sides are: `16,16,24`

Solution 2

The equal sides of the larger triangle are `24` units long.
This implies that the scale is: `k=24/12=2`.
So the base is `2*18=36` units long.

The triangle's sides are then: `24,24,36`.