Question

question quadrilateral hjk is similar to quadrilateral lmno. find the measure of side ol. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify corresponding sides

Since quadrilateral $HIJK$ is similar to quadrilateral $LMNO$, the ratios of corresponding - sides are equal. Let's assume that side $HK$ corresponds to side $LO$.

Step2: Set up the proportion

Let the length of $OL$ be $x$. The ratio of the sides of similar quadrilaterals gives us the proportion $\frac{HK}{LO}=\frac{JK}{NO}$. We know that $HK = 49$, $JK = 31$, and $NO = 9$. So, $\frac{49}{x}=\frac{31}{9}$.

Step3: Cross - multiply and solve for $x$

Cross - multiplying gives us $31x=49\times9$. Then $31x = 441$. Solving for $x$, we have $x=\frac{441}{31}\approx14.2$.

Answer:

$14.2$