# Triangle A has sides of lengths 36 , 48 , and 18 . Triangle B is similar to triangle A and has a side of length 3 . What are the possible lengths of the other two sides of triangle B?

Sep 24, 2016

$\left(3 , 4 , \frac{3}{2}\right) , \left(\frac{9}{4} , 3 , \frac{9}{8}\right) , \left(6 , 8 , 3\right)$

#### Explanation:

Any of the 3 sides of triangle B could be of length 3 hence there are 3 different possibilities for the sides of B.

Since the triangles are similar then the $\textcolor{b l u e}{\text{ratios of corresponding sides are equal}}$

Let the 3 sides of triangle B be a ,b and c, corresponding to the sides 36 ,48 and 18 in triangle A.
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If side a = 3 then ratio of corresponding sides $= \frac{3}{36} = \frac{1}{12}$

hence side b $= 48 \times \frac{1}{12} = 4 \text{ and side c} = 18 \times \frac{1}{12} = \frac{3}{2}$

The 3 sides of B would be $\left(3 , \textcolor{red}{4} , \textcolor{red}{\frac{3}{2}}\right)$
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If side b = 3 then ratio of corresponding sides $\frac{3}{48} = \frac{1}{16}$

a $= 36 \times \frac{1}{16} = \frac{9}{4} \text{ and side c} = 18 \times \frac{1}{16} = \frac{9}{8}$

The 3 sides of B would be $= \left(\textcolor{red}{\frac{9}{4}} , 3 , \textcolor{red}{\frac{9}{8}}\right)$
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If side c = 3 then ratio of corresponding sides $= \frac{3}{18} = \frac{1}{6}$

hence $a = 36 \times \frac{1}{6} = 6 \text{ and b} = 48 \times \frac{1}{6} = 8$

The 3 sides of B would be $= \left(\textcolor{red}{6} , \textcolor{red}{8} , 3\right)$
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