Question

Question was provided via image upload.

Explanation:

Step1: Identify similar triangles

$\triangle GHF \sim \triangle EGF \sim \triangle EGH$ (right triangle altitude similarity theorem)

Step2: Set up proportion for HF

Use $\triangle GHF \sim \triangle EGF$:
$\frac{HF}{GF} = \frac{GF}{EF}$

Step3: Substitute known values

$GF=20$, $EF=25$:
$\frac{HF}{20} = \frac{20}{25}$

Step4: Solve for HF

Multiply both sides by 20:
$HF = \frac{20 \times 20}{25} = \frac{400}{25}$

Answer:

16.0