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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