Question

1. 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. The side $BC$ corresponds to $RP$, and $AB$ corresponds to $QR$, and $AC$ corresponds to $QP$.

Step2: Set up the proportion

We know that $\frac{AB}{QR}=\frac{BC}{RP}=\frac{AC}{QP}$. We are given $AB = 4$ cm, $BC = 5$ cm, $QR = 8$ cm. Let $RP=x$. Then $\frac{AB}{QR}=\frac{BC}{RP}$, substituting the values we get $\frac{4}{8}=\frac{5}{x}$.

Step3: Solve the proportion

Cross - multiply: $4x=5\times8$. So $4x = 40$. Divide both sides by 4: $x=\frac{40}{4}=10$.

Answer:

10