# Triangle A has sides of lengths 28 , 36 , and 48 . Triangle B is similar to triangle A and has a side of length 12 . What are the possible lengths of the other two sides of triangle B?

Aug 26, 2016

Increase or decrease the sides of A by the same ratio.

#### Explanation:

The sides of Similar triangles are in the same ratio.

The side of 12 in triangle B could correspond with any of the three angles in triangle A.
The other sides are found by increasing or decreasing 12 in the same ratio as the other sides.

There are 3 options for the other two sides of Triangle B:

Triangle A :$\textcolor{w h i t e}{\times \times} 28 \textcolor{w h i t e}{\times \times \times \times x} 36 \textcolor{w h i t e}{\times \times \times \times x} 48$

Triangle B:
$\textcolor{w h i t e}{\times \times \times \times \times x} 12 \textcolor{w h i t e}{\times \times \times \times} \textcolor{red}{12} \times \frac{36}{28} \textcolor{w h i t e}{\times \times x} 12 \times \frac{48}{28}$

$\textcolor{w h i t e}{\times \times \times \times} \rightarrow \textcolor{red}{12} \textcolor{w h i t e}{\times \times \times \times x} 15 \frac{3}{7} \textcolor{w h i t e}{\times \times \times x} 20 \frac{4}{7}$

$A \div 3 \textcolor{w h i t e}{\times \times} \rightarrow \frac{28}{3} \textcolor{w h i t e}{\times \times \times \times x} \textcolor{red}{12} \textcolor{w h i t e}{\times \times \times \times x} 16$

$A \div 4 \textcolor{w h i t e}{\times \times} \rightarrow 7 \textcolor{w h i t e}{\times \times \times \times \times x} 9 \textcolor{w h i t e}{\times \times \times \times x} \textcolor{red}{12}$