# Triangle A has sides of lengths 42 ,36 , and 21 . Triangle B is similar to triangle A and has a side of length 14 . What are the possible lengths of the other two sides of triangle B?

Jan 12, 2017

The possible length of sides for triangle B are $\left\{14 , 12 , 7\right\}$, $\left\{14 , \frac{49}{3} , \frac{49}{6}\right\}$,$\left\{14 , 28 , 24\right\}$

#### Explanation:

Let say 14 is a length of triangle B reflect to the length of 42 for triangle A and X,Y are the length for other two sides of triangle B.

$\frac{X}{36} = \frac{14}{42}$
$X = \frac{14}{42} \cdot 36$
$X = 12$

$\frac{Y}{21} = \frac{14}{42}$
$Y = \frac{14}{42} \cdot 21$
$Y = 7$
The length of sides for triangle B are $\left\{14 , 12 , 7\right\}$

Let say 14 is a length of triangle B reflect to the length of 36 for triangle A and X,Y are the length for other two sides of triangle B.
$\frac{X}{42} = \frac{14}{36}$
$X = \frac{14}{36} \cdot 42$
$X = \frac{49}{3}$

$\frac{Y}{21} = \frac{14}{36}$
$Y = \frac{14}{36} \cdot 21$
$Y = \frac{49}{6}$
The length of sides for triangle B are $\left\{14 , \frac{49}{3} , \frac{49}{6}\right\}$

Let say 14 is a length of triangle B reflect to the length of 21 for triangle A and X,Y are the length for other two sides of triangle B.
$\frac{X}{42} = \frac{14}{21}$
$X = \frac{14}{21} \cdot 42$
$X = 28$

$\frac{Y}{36} = \frac{14}{21}$
$Y = \frac{14}{21} \cdot 36$
$Y = 24$
The length of sides for triangle B are $\left\{14 , 28 , 24\right\}$