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: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let $QO = x$. We have the proportion $\frac{LM}{PQ}=\frac{LN}{QO}$. Assume $LM = 14$, $PQ = 47$, $LN=25$. So $\frac{14}{47}=\frac{25}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $14x=47\times25$.

Step3: Calculate the right - hand side

$47\times25 = 1175$, so $14x = 1175$.

Step4: Solve for x

$x=\frac{1175}{14}\approx83.9$.

Answer:

$83.9$