# Triangle A has sides of lengths 60 , 45 , and 54 . Triangle B is similar to triangle A and has a side of length 7 . What are the possible lengths of the other two sides of triangle B?

Apr 12, 2016

$\left(7 , \frac{21}{4} , \frac{63}{10}\right) , \left(\frac{28}{3} , 7 , \frac{42}{5}\right) , \left(\frac{70}{9} , \frac{35}{6} , 7\right)$

#### 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 60 , 45 and 54 in triangle A.
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If side a = 7 then the ratio of corresponding sides $= \frac{7}{60}$
hence b =$45 \times \frac{7}{60} = \frac{21}{4} \text{ and } c = 54 \times \frac{7}{60} = \frac{63}{10}$
The 3 sides of B $= \left(7 , \frac{21}{4} , \frac{63}{10}\right)$
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If b = 7 then ratio of corresponding sides $= \frac{7}{45}$
hence a $= 60 \times \frac{7}{45} = \frac{28}{3} \text{ and } c = 54 \times \frac{7}{45} = \frac{42}{5}$
The 3 sides of B = $\left(\frac{28}{3} , 7 , \frac{42}{5}\right)$
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If c = 7 then ratio of corresponding sides = $\frac{7}{54}$
hence a $= 60 \times \frac{7}{54} = \frac{70}{9} \text{ and } b = 45 \times \frac{7}{54} = \frac{35}{6}$
The 3 sides of B $= \left(\frac{70}{9} , \frac{35}{6} , 7\right)$
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