If the area of ΔABC is , what is the length of AB?

Question

https://gmatclub.com/forum/download/file.php?id=28754 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 2015-12-27_2136.png

peachfuzz · Answer

I believe the area is missing from the question stem

EMPOWERgmatRichC · Answer

Hi Bunuel,

The prompt is missing the total area (and while there are plenty of smart people here, correctly answering this question without that information will be difficult).

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

Sorry. Edited. Thank you for noticing.

appsy01 · Answer

1/2 * BC * AB = 8\sqrt{3} => BC * AB = 16\sqrt{3}

BC = \frac{Hyp}{2} and AB = \frac{Hyp}{2 *} \sqrt{3}

Comparing
 \frac{x}{2} * \frac{x}{2}\sqrt{3} = 4 * 4\sqrt{3} =>\frac{x}{2} * \frac{x}{2} \sqrt{3} = \frac{8}{2} * \frac{8}{2}\sqrt{3}

Therefore x=8

TeamGMATIFY · Answer

Area =  \frac{1}{2} *AC*BC

tan 60 = AC/BC
 \sqrt{3}  BC = AC

Area =  \frac{1}{2}  \sqrt{3}  BC * BC =  8\sqrt{3} 
Hence BC = 4

Cos 60 = BC/AB
AB = BC/Cos 60 = BC/(1/2) = 2BC = 8

Option E

nipunjain14 · Answer

This is an 30- 60 -90 triangle so the lengths of the sides will be i nratio:
 x(sqrt(3)) : x: 2x

Area given is 8(sqrt(3))
1/2 * x(sqrt(3)) * x = 8(sqrt(3))

thus x = 4
since BC = 2x => 8

Ans:E

generis · Answer

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 = x

Let 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

cbh · Answer

Area ABC = 1/2*AC*BC
so 8√3 * 2 = AB * BC = 16√3
the relation of triangle sides is 1 to √3 to 2
then x * x√3 = (x^2)√3 = 16√3
so x = BC = 4
then AC = 4√3

=>> AC^2+BC^2=AB^2
(4√3)^2+4^2=64
AB = √64 = 8

bumpbot · Answer

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If the area of ΔABC is , what is the length of AB?

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If the area of ΔABC is , what is the length of AB?

Prep Toolkit

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