# Triangle A has sides of lengths 15 , 12 , and 12 . 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?

Mar 14, 2016

$\left(24 , \frac{96}{5} , \frac{96}{5}\right) , \left(30 , 24 , 24\right) , \left(30 , 24 , 24\right)$

#### Explanation:

Since the triangles are similar the the ratios of corresponding sides are equal.

Name the 3 sides of triangle B , a , b and c , corresponding to the sides 15 , 12 and 12 in triangle A.
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If side a = 24 then ratio of corresponding sides$= \frac{24}{15} = \frac{8}{5}$
hence b = c $= 12 \times \frac{8}{5} = \frac{96}{5}$
The 3 sides in B $= \left(24 , \frac{96}{5} , \frac{96}{5}\right)$
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If b = 24 then ratio of corresponding sides $= \frac{24}{12} = 2$
hence a = 15xx2 = 30 " and c = 2xx12 = 24

The 3 sides of B = (30,24,24)
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If c = 24 will give the same result as b = 24