Question

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

Explanation:

Step1: Identify corresponding sides

Since quadrilateral \( FGHI \) is similar to quadrilateral \( JKLM \), the ratio of corresponding sides is equal. The side \( IH = 31 \) in \( FGHI \) corresponds to side \( ML = 7 \) in \( JKLM \), and side \( HG = 43 \) in \( FGHI \) corresponds to side \( LK \) (which is \( KL \)) in \( JKLM \).

Step2: Set up the proportion

Let \( KL = x \). The proportion of corresponding sides is \(\frac{IH}{ML}=\frac{HG}{KL}\), so \(\frac{31}{7}=\frac{43}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 31x=7\times43 \). Calculate \( 7\times43 = 301 \). Then \( x=\frac{301}{31}\approx9.7 \).

Answer:

\( 9.7 \)