see attached If |AB| is 15 and |AC| is 36, what is

Question

see attached



If |AB| is 15 and |AC| is 36, what is the area in square units of the shaded isosceles triangle if 
 /  CBE = 105 degrees ?

(A) 1501 (B) 1521 (C) 1541 (D) 1561 (E) 1581

GMATT73 · Answer

Helps to memorize our special triangles here: 5-12-13 <=> 15-36-39

39 makes a nice equilateral triangle within the rhombus, which we can use to calculate the area of the shaded region ---> 39^2=1521

(B)

1:45

ps_dahiya · Answer

I don't see any equilateral triangle here :roll:

My way is BC = 39 using pythagorus Then 39/BD = Cos60 so BD = 78 BE = DE = x so x^2 + x^2 = 78^2 x^2 = (78^2)/2 We need to find 1/2 * x^2 = (78^2)/(2*2) = 39^2 = 1521

haas_mba07 · Answer

(B) 1521

Given AB = 15, AC = 36

Therefore BC = 39 (5-12-13 Triangle)

As triangle BDE is 45-45-90 
Angle CBD = 60 => CDB = 30

Triangle CBD is 30-60-90 triangle.

Sides are x : x*sqrt(3): 2x 

As BD= 2x39 which gives 
BE = 2x39/sqrt(2)

As BDE is 45-45-90 sides are in the ratio 1:1:sqrt(2)

Area = 1/2 x base x height 
= 1/2 x 2x39 x 2 x 39 / 2 = 39 x39 = 1521.

rnachloo · Answer

I got the exact same result, but took me about 10 minutes to solve the problem.

Is it a real GMAT question? Are there any shortcuts?

haas_mba07 · Answer

It isn't a quick question by any means but you should still be able to squeeze through this problem. 

 As for the time taken, more practice with a set of tougher questions will improve your speed on all questions. 

Is it a GMAT-like question? .. Probably not.

kevincan · Answer

It shouldn't/needn't take you 10 minutes! 

Remember: know your  special right triangles 

a:b:c

3:4:5
5:12:13
1:1: sqrt (2)
1:sqrt(3):2

Also if a  isosceles triangle has hypotenuse h, the area is h^2/4 

So the area of shaded tiangle is ((39)(2)^2)/4 =39^2= 1600-80+1=1521

jaynayak · Answer

From the question we can find out that triangle BCD is a 30-60-90 traingle.
BC^2 = 36^2 + 15^2 = 1521 = 39

Now since triangle BCD is a 30-60-90 , BD = 2*39

Since BDE is an issoceles right traingle,

BD = BEsqr(2)

2*39 = BE Sqr(2)
BE = 39sqr(2)

Area = 1/2 *  ^2
 = 39^2 = 1521

see attached If |AB| is 15 and |AC| is 36, what is

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