Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side KL. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
The corresponding sides of similar figures are in proportion.
So we can set up the following equation using the ratio of corresponding sides:
$\frac{FG}{JK} = \frac{GH}{KL} = \frac{HI}{LM}$
We are given that FG = 5, GH = 7, HI = 8, JK = 10, and LM = 15.
Plugging the values into the equation, we get:
$\frac{5}{10} = \frac{7}{KL} = \frac{8}{15}$
Solving for KL, we have:
$\frac{7}{KL} = \frac{5}{10}$
$7 \cdot 10 = 5 \cdot KL$
$70 = 5KL$
$KL = \frac{70}{5}$
$KL = 14$
Therefore, the measure of side KL is 14.