Question

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

Explanation:

Step1: Identify corresponding sides

Since quadrilateral JKLM ~ NOPQ, sides JK and NO correspond, and sides MJ and QN correspond. So, the ratios of corresponding sides are equal: $\frac{MJ}{QN} = \frac{JK}{NO}$.

Step2: Substitute known values

We know MJ = 23, JK = 17.6, NO = 53. Let QN = x. Then $\frac{23}{x} = \frac{17.6}{53}$.

Step3: Solve for x

Cross - multiply: $17.6x = 23\times53$. Calculate $23\times53 = 1219$. Then $x=\frac{1219}{17.6}$.

Step4: Compute the value

$\frac{1219}{17.6}\approx69.26136\approx69.3$ (rounded to the nearest tenth).

Answer:

The measure of side QN is approximately 69.3.