Question

the pentagons abcde and pqrst are similar. find the length x of $overline{qr}$.

Explanation:

Step1: Set up proportion

Since the pentagons are similar, the ratios of corresponding - side lengths are equal. We can set up the proportion using the corresponding sides $BC$ and $QR$, and $AE$ and $PT$. The proportion is $\frac{BC}{QR}=\frac{AE}{PT}$. Substituting the given values, we have $\frac{4}{x}=\frac{3}{3.6}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{4}{x}=\frac{3}{3.6}$ gives us $3x = 4\times3.6$.

Step3: Solve for $x$

First, calculate $4\times3.6 = 14.4$. Then, we have the equation $3x=14.4$. Divide both sides of the equation by 3: $x=\frac{14.4}{3}=4.8$.

Answer:

$4.8$