Question

quadrilateral hijk is similar to quadrilateral lmno. find the measure of side no. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify similar sides

Since quadrilateral HIJK ~ L MNO, corresponding sides are proportional. Side HI (length 5) corresponds to side LM (length 21), and side JK (length 8) corresponds to side NO (let's call it \( x \)).

Step2: Set up proportion

The proportion is \( \frac{HI}{LM} = \frac{JK}{NO} \), so \( \frac{5}{21} = \frac{8}{x} \).

Step3: Solve for \( x \)

Cross - multiply: \( 5x = 21\times8 \). Calculate \( 21\times8 = 168 \). Then \( x=\frac{168}{5}=33.6 \).

Answer:

33.6