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.

Answer 1

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.