triangle GMATPrep question

Question

quick one guys.

There are two triangles with similiar degree angles. Area of one is 2x the other. What is the value of the base of S (the bigger triangle) is terns of the base of the triangle s (the smaller triangle)

a) sqrt2/2 s
b) sqrt3/2 s
c) sqrt2 s
d) sqrt3 s
e) 2s

this one is tricky

Dan

XxxyyY · Answer

-C-
Since both triangles are similar, both angles are equal and each length is proportional. 
So, s/S = h/H or H/h=S/s

(s*h)(1/2)(2)=(S*H)(1/2) --> (s*h)=(S*H)(1/2)
(S*H)/(s*h)=2 --> S/s*H/h=2 --> S/s*S/s=2 , 
solving for S --> S^2/s^2=2 = S=sqrt2s

DreamMBA · Answer

Agree with X & Y above

Andr359 · Answer

Area of smaller triangle: bh
Area of bigger triangle: BH = 2bh
As both triangles have the same interior angles, they are proportional, so if B is n times larger than b, H is also n times larger than h => BH = n^2 * bh = 2bh => n = sqrt(2) => C.

svas · Answer

i used a right angle triangle (45 45 90) to solve this. bcos then we know base and height are same for such a triangle.

for first right angle : 1, 1, sqrt2
for second right angel : b, b, b*sqrt2
==> 1/2 * 2 = 1/2 b*b
==> new b= sqrt 2
so ratio sqrt2 :1

ProfessorMMA · Answer

If the formulaic proof doesn't come to mind quickly enough, sometimes just plugging numbers in can work. Here, start with a right triangle with base and height of 1. With that setup, you can pretty quickly deduce that the base and height of the big right triangle has to be Sqrt(2).

triangle GMATPrep question

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