# Triangle A has sides of lengths 18 , 12 , and 21 . 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 19, 2018

$\Delta \left(24 , a , b\right)$

$\Delta \left(24 , c , d\right)$

$\Delta \left(24 , e , f\right)$

#### Explanation:

$\left\{\frac{18}{24} = \frac{12}{a} = \frac{21}{b}\right\} \mathmr{and}$
$\left\{\frac{18}{c} = \frac{12}{24} = \frac{21}{d}\right\} \mathmr{and} \left\{\frac{18}{e} = \frac{12}{f} = \frac{21}{24}\right\}$

$a = 24 \cdot \frac{12}{18} = 16$

$b = 24 \cdot \frac{21}{18} = 28$

$c = 18 \cdot \frac{24}{12} = 36$

$d = 24 \cdot \frac{21}{12} = 42$

$e = 18 \cdot \frac{24}{21} = \frac{144}{7}$

$f = 12 \cdot \frac{24}{21} = \frac{96}{7}$