# Triangle A has sides of lengths 24 , 15 , and 18 . 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?

Jun 2, 2017

Possibility 1: 15 and 18
Possibility 2: 20 and 32
Possibility 3: 38.4 and 28.8

#### Explanation:

First we define what a similar triangle is. A similar triangle is one in which either the corresponding angles are the same, or the corresponding sides are the same or in proportion.

In the 1st possibility, we assume that the length of the sides of triangle $B$ didn't change, so the original lengths are kept, 15 and 18, keeping the triangle in proportion and thus similar.

In the 2nd possibility, we assume that the length of one side of triangle $A$, in this case length 18, has been multiplied up to 24. To find the rest of the values, we first divide $\frac{24}{18}$ to get $1 \frac{1}{3}$. Next, we multiply both $24 \cdot 1 \frac{1}{3}$ and $15 \cdot 1 \frac{1}{3}$, and we do this to keep the triangle in proportion and thus similar. So, we get the answers of 20 and 32

In the 3rd possibility we do the exact same thing, except using the number 15. So we divide $\frac{24}{15} = 1.6$, multiply $24 \cdot 1.6$ and $18 \cdot 1.6$ to get 38.4 and 28.8. Again, this is done to keep the sides in proportion, and thus the triangle is made similar.