Quadrilateral JKLM is similar to quadrilateral NOPQ. We are asked to find the measure of side OP, given that LM = 17, JM = 11, and NQ = 53. We are asked to round to the nearest tenth if necessary.

1. Problem Description

Quadrilateral JKLM is similar to quadrilateral NOPQ. We are asked to find the measure of side OP, given that LM = 17, JM = 11, and NQ =

5

3. We are asked to round to the nearest tenth if necessary.

2. Solution Steps

Since the quadrilaterals JKLM and NOPQ are similar, their corresponding sides are proportional. Specifically, quadrilateral JKLM corresponds to quadrilateral NOPQ in that order of letters, so we have:

$\frac{JM}{OP} = \frac{LM}{NQ}$

We are given $JM = 11$, $LM = 17$, and $NQ = 53$. Let $OP = x$.

Then,

$\frac{11}{x} = \frac{17}{53}$

Cross-multiplying, we get:

$17x = 11 \times 53$

$17x = 583$

$x = \frac{583}{17}$

$x \approx 34.294$

Rounding to the nearest tenth, we get $x \approx 34.3$.

3. Final Answer

The measure of side OP is approximately 34.3.