Question

triangle lmn is similar to triangle opq. find the measure of side qo. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since $\triangle LMN \sim \triangle OPQ$, the ratios of corresponding sides are equal. Let's assume $LM$ corresponds to $OP$, and $LN$ corresponds to $OQ$ (or $QO$). So, $\frac{LM}{OP}=\frac{LN}{QO}$.

Given $LM = 5$, $OP = 21$, $LN = 11$. Let $QO = x$.

Step2: Set up proportion and solve

Set up the proportion: $\frac{5}{21}=\frac{11}{x}$

Cross - multiply: $5x=21\times11$

Calculate $21\times11 = 231$, so $5x = 231$

Then $x=\frac{231}{5}=46.2$

Answer:

46.2