# Triangle A has sides of lengths 36 , 44 , and 32 . Triangle B is similar to triangle A and has a side of length 4 . What are the possible lengths of the other two sides of triangle B?

Jan 20, 2018

Possible lengths of other two sides of triangle B are

Case 1 : $4.8889 , 3.5556$

Case 2 : $3.2727 , 2.9091$

Case 3 : $4.5 , 5.5$

#### Explanation:

Let the sides be a1, a2, a3 of $\Delta$A and b1, b2, b3 of $\Delta$ B.

We know,

$\frac{a 1}{b 1} = \frac{a 2}{b 2} = \frac{a 3}{b 3}$

Given $a 1 = 36 , a 2 = 44 , a 3 = 32$

Case 1 :
$b 1 = 4$

Then $b 2 = \frac{\left(a 2\right) \cdot \left(b 1\right)}{a 1} = \frac{44 \cdot 4}{36} = 4.8889$

$b 3 = \frac{\left(a 3\right) \cdot \left(b 1\right)}{a 1} = \frac{32 \cdot 4}{36} = 3.5556$

Case 2 :
$b 2 = 4$

$b 1 = \frac{\left(a 1\right) \cdot \left(b 2\right)}{a 2} = \frac{36 \cdot 4}{44} = 3.2727$

$b 3 = \frac{32 \cdot 4}{44} = 2.9091$

Case 3 :

$b 3 = 4$

$b 1 = \frac{36 \cdot 4}{32} = 4.5$

$b 2 = \frac{44 \cdot 4}{32} = 5.5$