Question

the pentagons abcde and jklmn are similar. find the length x of $overline{mn}$.

Explanation:

Step1: Set up proportion

For similar polygons, the ratios of corresponding - sides are equal. The ratio of the side lengths of the two similar pentagons is the same for all corresponding sides. We can set up the proportion using the corresponding sides $\frac{AE}{JN}=\frac{DE}{MN}$.
We know that $AE = 2$, $JN=1.4$, $DE = 6$, and $MN=x$. So the proportion is $\frac{2}{1.4}=\frac{6}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{2}{1.4}=\frac{6}{x}$ gives us $2x=1.4\times6$.

Step3: Solve for x

First, calculate $1.4\times6 = 8.4$. Then, we have the equation $2x = 8.4$. Divide both sides of the equation by 2: $x=\frac{8.4}{2}=4.2$.

Answer:

$4.2$