# Triangle A has sides of lengths 32 , 40 , and 16 . Triangle B is similar to triangle A and has a side of length 8 . What are the possible lengths of the other two sides of triangle B?

Sep 30, 2016

Three possible lengths of other two sides are $\left(16 , 20\right) \mathmr{and} \left(4 , 10\right) \mathmr{and} \left(3.2 , 6.4\right)$ unit each

#### Explanation:

The ratio of sides of triangle A is $\frac{16}{8} : \frac{32}{8} : \frac{40}{8} \mathmr{and} 2 : 4 : 5$
The ratio of sides of similar triangle B must have the same ratio.
If $8$ be the lowest side then other two sides are $4 \cdot \frac{8}{2} = 16 \mathmr{and} 5 \cdot \frac{8}{2} = 20$ unit
If $8$ be the middle one then other two sides are $2 \cdot \frac{8}{4} = 4 \mathmr{and} 5 \cdot \frac{8}{4} = 10$ unit
if $8$ be the biggest side then other two sides are $2 \cdot \frac{8}{5} = 3.2 \mathmr{and} 4 \cdot \frac{8}{5} = 6.4$unit
Hence three possible lengths of other two sides are $\left(16 , 20\right) \mathmr{and} \left(4 , 10\right) , \mathmr{and} \left(3.2 , 6.4\right)$ unit each [Ans]