The figure shows a right triangle ABC with

[Max@Math Revolution]

[GMAT math practice question]

The figure shows a right triangle ABC with ∠A = 90, BH = 8, and CH = 4. Moreover, AH and BC are perpendicular to each other. What is the length of AH?

A. \(\sqrt{2}\)
B. 3 \(\sqrt{2}\)
C. 4 \(\sqrt{2}\)
D. 3
E. 4

[Max@Math Revolution]

=>

Since triangles ABH and CAH are similar to each other, we have AH:BH = CH:AH.
Thus, we have x:8 = 4:x or x^2 = 32 and x = 4 √2.

Therefore, C is the answer.
Answer: C