Question

in the figure below, △abc~△qrp. enter the number in the box. pr = cm

Explanation:

Step1: Identify corresponding sides

Since $\triangle ABC\sim\triangle QRP$, the ratios of corresponding sides are equal. Side $BC$ corresponds to side $RP$, and side $AC$ corresponds to side $QP$.

Step2: Set up proportion

We have $\frac{BC}{RP}=\frac{AC}{QP}$. Given $BC = 5$ cm, $AC = 4$ cm, and $QP=8$ cm. Let $RP = x$. Then $\frac{5}{x}=\frac{4}{8}$.

Step3: Cross - multiply and solve

Cross - multiplying gives $4x=5\times8$. So $4x = 40$, and $x=\frac{40}{4}=10$.

Answer:

$10$