# 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?

Jul 22, 2017

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: $k = \frac{24}{18} = \frac{4}{3}$.
If the scale is $k = \frac{4}{3}$, then the equal sides would be $\frac{4}{3} \cdot 12 = 16$ 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: $k = \frac{24}{12} = 2$.
So the base is $2 \cdot 18 = 36$ units long.

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