Question

in the figure below, triangle ghi is similar to triangle mhl.
what is the distance between m and h?

Explanation:

Step1: Identify corresponding sides

Corresponding sides: $GH=24$, $IH=16$, $LH=18$, $MH=x$
Ratio: $\frac{GH}{IH} = \frac{LH}{MH}$
$\frac{24}{16} = \frac{18}{x}$

Step2: Simplify ratio and solve for x

Simplify $\frac{24}{16} = \frac{3}{2}$
$\frac{3}{2} = \frac{18}{x}$
Cross multiply: $3x = 36$
$x = 12$

Answer:

12