Question

quadrilateral jklm is similar to quadrilateral nopq. find the measure of side op. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up proportion

Since the quadrilaterals are similar, the ratios of corresponding sides are equal. Let the side corresponding to $OP$ in the first - quadrilateral be $KL = 23$, and the side corresponding to $PQ=49$ in the first - quadrilateral be $ML = 11$. The proportion is $\frac{OP}{KL}=\frac{PQ}{ML}$.

Step2: Substitute values

Substitute $KL = 23$, $PQ = 49$, and $ML = 11$ into the proportion: $\frac{OP}{23}=\frac{49}{11}$.

Step3: Solve for $OP$

Cross - multiply to get $11\times OP=49\times23$. Then $OP=\frac{49\times23}{11}=\frac{1127}{11}\approx102.5$.

Answer:

$102.5$