Question

1. triangle mno is similar to triangle pqr. find the measure of side rp. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since $\triangle MNO\sim\triangle PQR$, the ratios of corresponding - sides are equal. Let $RP = x$. The corresponding sides give the proportion $\frac{MN}{PQ}=\frac{OM}{RP}$. We assume $MN = 7$, $OM = 15$, and $PQ = 33$. So, $\frac{7}{33}=\frac{15}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{7}{33}=\frac{15}{x}$ gives us $7x=15\times33$.

Step3: Solve for $x$

First, calculate $15\times33 = 495$. Then, $x=\frac{495}{7}\approx70.7$.

Answer:

$70.7$