Question

quadrilateral defg is similar to quadrilateral hijk. find the measure of side jk. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify corresponding sides

Since quadrilateral DEFG ~ HIJK, side DG (55) corresponds to side HK (16.9), and side GF (28) corresponds to side JK (let's call it \( x \)).

Step2: Set up proportion

For similar figures, the ratios of corresponding sides are equal. So, \(\frac{DG}{HK} = \frac{GF}{JK}\)

Substitute the known values: \(\frac{55}{16.9} = \frac{28}{x}\)

Step3: Solve for \( x \)

Cross - multiply: \( 55x = 28\times16.9 \)

First, calculate \( 28\times16.9 = 473.2 \)

Then, \( x=\frac{473.2}{55}\approx8.6 \)

Answer:

\( 8.6 \)