Question

quadrilateral fghi is similar to quadrilateral jklm. find the measure of side kl. round your answer to the nearest tenth if necessary.
i h m l
31 7
43 j k
f g

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals \( FGHI \) and \( JKLM \) are similar, the ratio of corresponding sides is equal. Side \( IH \) in \( FGHI \) (length 31) corresponds to side \( ML \) in \( JKLM \) (length 7). Side \( HG \) in \( FGHI \) (length 43) corresponds to side \( LK \) (which we need to find, let's call it \( x \)) in \( JKLM \).

Step2: Set up proportion

The proportion of corresponding sides is \(\frac{IH}{ML}=\frac{HG}{LK}\). Substituting the known values: \(\frac{31}{7}=\frac{43}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 31x = 43\times7 \). Calculate \( 43\times7 = 301 \). Then \( x=\frac{301}{31}\approx9.7 \).

Answer:

\( 9.7 \)