Question

quadrilateral ghij is similar to quadrilateral klmn. find the measure of side nk. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals GHIJ and KLMN are similar, the ratios of corresponding sides are equal. Side IJ (length 5) in GHIJ corresponds to side MN (length 22) in KLMN, and side JG (length 11) in GHIJ corresponds to side NK (let's call its length \( x \)) in KLMN.

Step2: Set up proportion

The proportion of corresponding sides is \(\frac{IJ}{MN} = \frac{JG}{NK}\). Substituting the known values: \(\frac{5}{22} = \frac{11}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \(5x = 22\times11\). Calculate \(22\times11 = 242\). Then \(x=\frac{242}{5}=48.4\).

Answer:

48.4