Bunuel wrote:

If the area of ΔABC is \(8\sqrt{3}\), what is the length of AB?

A. 4

B. 5

C. 6

D. 7

E. 8

Attachment:

2015-12-27_2136.png

The missing angle A must be 30°

I have a hard time tracking on side names, so I use terms such as "short leg."

30-60-90 right triangles have sides in ratio

short leg: long leg: hypotenuse \(x: x\sqrt{3}: 2x\)

Let short leg BC =

base = xLet long leg AC =

height=\(x\sqrt{3}\)Area Δ = \(\frac{b*h}{2}\), given as \(8\sqrt{3}\)

\(\frac{x * x\sqrt{3}}{2}\)=\(8\sqrt{3}\)

\(16\sqrt{3}\) = \(x * x\sqrt{3}\)

Divide by \(\sqrt{3}\)

16 = x\(^2\)

x = 4

That's the short leg. Hypotenuse AB length is twice that, 2x = 8.

Answer E

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