Question

$∆ABC$is similar to $∆XYZ$. The lengths of two sides of each triangle are given in the figure. Find the length of the third sides.

Short answer

The value for the side$b$is$9$and the value for the side$x$is$2\frac{1}{3}$.

Step-by-step solution

Step 1. Given information.

The given figure is:

Step 2. To find the value of b.

Since the given triangles are similar, the corresponding angle measures are equal and their corresponding sides have the same ratio.

$\begin{array}{rcl}\frac{8}{2{\displaystyle \frac{2}{3}}}& =& \frac{b}{3}\\ \frac{8}{{\displaystyle \frac{8}{3}}}& =& \frac{b}{3}\\ \frac{8\times 3}{8}& =& \frac{b}{3}\\ 3& =& \frac{b}{3}\\ b& =& 3\times 3\\ b& =& 9\end{array}$

Step 3. To find the value of x.

Since the given triangles are similar, the corresponding angle measures are equal and their corresponding sides have the same ratio.

$\begin{array}{rcl}\frac{8}{2{\displaystyle \frac{2}{3}}}& =& \frac{7}{x}\\ \frac{8}{{\displaystyle \frac{8}{3}}}& =& \frac{7}{x}\\ \frac{8\times 3}{8}& =& \frac{7}{x}\\ 3& =& \frac{7}{x}\\ x& =& \frac{7}{3}\\ x& =& 2\frac{1}{3}\end{array}$

Step 4. Simplified answer.

Hence, the required solution is$b=9$and$x=2\frac{1}{3}$.