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The figure shows a right triangle ABC with

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The figure shows a right triangle ABC with

by Max@Math Revolution » Thu Apr 02, 2020 12:17 am

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[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?
4.2PS.png
A. \(\sqrt{2}\)
B. 3 \(\sqrt{2}\)
C. 4 \(\sqrt{2}\)
D. 3
E. 4
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Re: The figure shows a right triangle ABC with

by Max@Math Revolution » Mon Apr 06, 2020 2:45 am
=>

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
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