# Triangle A has sides of lengths 12 ,1 4, and 11 . Triangle B is similar to triangle A and has a side of length 4 . What are the possible lengths of the other two sides of triangle B?

Jan 23, 2017

the other two sides are: 1) $\frac{14}{3} \mathmr{and} \frac{11}{3}$ or 2) $\frac{24}{7}$ and $\frac{22}{7}$ or 3) $\frac{48}{11}$ and $\frac{56}{11}$

#### Explanation:

Since B and A are similar their sides are in the following possible ratios:

$\frac{4}{12} \mathmr{and} \frac{4}{14} \mathmr{and} \frac{4}{11}$

1) ratio$= \frac{4}{12} = \frac{1}{3}$: the other two sides of A are $14 \cdot \frac{1}{3} = \frac{14}{3}$ and $11 \cdot \frac{1}{3} = \frac{11}{3}$

2) ratio$= \frac{4}{14} = \frac{2}{7}$: the other two sides are $12 \cdot \frac{2}{7} = \frac{24}{7}$ and $11 \cdot \frac{2}{7} = \frac{22}{7}$

3) ratio$= \frac{4}{11}$: the other two sides are $12 \cdot \frac{4}{11} = \frac{48}{11}$ and $14 \cdot \frac{4}{11} = \frac{56}{11}$