Question

quadrilateral ghlj 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 quadrilateral GHIJ is similar to quadrilateral KLMN, the ratio of corresponding sides is equal. Let's assume the side of length 5 in GHIJ corresponds to the side of length 22 in KLMN, and the side of length 11 in GHIJ corresponds to side NK in KLMN.

Step2: Set up the proportion

Let \( x \) be the length of NK. The proportion is \(\frac{11}{x}=\frac{5}{22}\) (because the ratio of corresponding sides of similar figures is equal).

Step3: Solve for \( x \)

Cross - multiply: \( 5x = 11\times22 \)
\( 5x=242 \)
Divide both sides by 5: \( x=\frac{242}{5}=48.4 \)

Answer:

48.4