Question

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

Explanation:

Step1: Identify corresponding sides

Since quadrilateral \( FGHI \) is similar to quadrilateral \( JKLM \), the sides \( IF \) and \( MJ \) are corresponding, and sides \( HI \) and \( LM \) are corresponding. So the ratio of corresponding sides is equal. Let \( LM = x \). The ratio of \( MJ \) to \( IF \) is \( \frac{26}{7} \), and the ratio of \( LM \) to \( HI \) is \( \frac{x}{9} \).

Step2: Set up proportion

Because of similarity, \( \frac{MJ}{IF}=\frac{LM}{HI} \), so \( \frac{26}{7}=\frac{x}{9} \).

Step3: Solve for \( x \)

Cross - multiply: \( 7x = 26\times9 \). Calculate \( 26\times9 = 234 \). Then \( x=\frac{234}{7}\approx33.4 \) (rounded to the nearest tenth).

Answer:

\( 33.4 \)