Question

find gh.
gh =
submit

Explanation:

Step1: Identify similarity ratio

The segments with arrows show that $HK \parallel IJ$, so $\triangle GHK \sim \triangle GIJ$. The ratio of corresponding sides is $\frac{GK}{GJ} = \frac{24}{36} = \frac{2}{3}$.

Step2: Set up proportion for GH

Let $GH = x$, then $GI = x + 22$. The similarity ratio gives $\frac{GH}{GI} = \frac{2}{3}$.
$$\frac{x}{x + 22} = \frac{2}{3}$$

Step3: Solve the equation

Cross-multiply to eliminate fractions:
$$3x = 2(x + 22)$$
Expand and simplify:
$$3x = 2x + 44$$
$$3x - 2x = 44$$
$$x = 44$$

Answer:

$44$