# Triangle A has sides of lengths 12 , 9 , and 6 . Triangle B is similar to triangle A and has a side with a length of 16 . What are the possible lengths of the other two sides of triangle B?

Apr 5, 2016

(16,12,8), (64/3,16,32/3 ) , (32,24,16)

#### Explanation:

Since the triangles are similar then the ratios of corresponding sides are equal.
Name the 3 sides of triangle B , a,b and c corresponding to the sides 12,9 and 6 in triangle A.
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If side a = 16 then ratio of corresponding sides $= \frac{16}{12} = \frac{4}{3}$

hence $b = 9 \times \frac{4}{3} = 12 \text{ and } c = 6 \times \frac{4}{3} = 8$

The 3 sides of B = (16 , 12 , 8 )
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If side b = 16 then ratio of corresponding sides $= \frac{16}{9}$

hence a =$12 \times \frac{16}{9} = \frac{64}{3} \text{ and } c = 6 \times \frac{16}{9} = \frac{32}{3}$

The 3 sides of B $= \left(\frac{64}{3} , 16 , \frac{32}{3}\right)$
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If c = 16 then ratio of corresponding sides = $\frac{16}{6} = \frac{8}{3}$

hence a$= 12 \times \frac{8}{3} = 32 \text{ and } b = 9 \times \frac{8}{3} = 24$

The 3 sides of B = (32 , 24 , 16 )
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