triangle lmn is similar to triangle opq. find the measure of side qo. round your answer to the nearest tenth…

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.

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.

Answer

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:

$83.9$