# Triangle A has sides of lengths 24 , 24 , and 20 . Triangle B is similar to triangle A and has a side with a length of 16 . What are the possible lengths of the other two sides of triangle B?

Oct 7, 2017

Lengths of other two sides of triangle B are $16$ & $13 \left(\frac{1}{3}\right)$

#### Explanation:

Triangle A & B are similar. Hence corresponding angles are equal and ratio of the corresponding sides are equal.
Let the vertices of Triangle A & B be PQR & XYZ respectively.

Given $P Q = 24 , Q R = 24$ & $R P = 20$
Also $\frac{P Q}{X Y} = \frac{Q R}{Y Z} = \frac{R P}{Z X}$

If $X Y = 16$ then
$\frac{24}{16} = \frac{24}{Y Z} = \frac{20}{Z} X$
$\therefore Y Z = \frac{24 \cdot 16}{24} = 16$
Similarly $Z X = \frac{20 \cdot 16}{24} = \frac{40}{3}$