gmat maths geometry

i assume the power of 2 such as a^2 below

quantskillsgmat wrote:If a and b are sides of a traingle and area of this triangle is given as 1/4(a^2+b^2).
what are angles of this traingle.
a)60-60-60
b)30-60-90
c)90-45-45
d)80-70-30
e_100-50-30

this is theoretical question, and we need to try out diff. triangles. I tried the right triangle at first and got it right

c

Not sure if the question is correct..

Area = 1/4 * (a^2 + b^2)

60-60-60 - let the side be '1' unit -> area = Sqrt(3)/4

1/4 * (a^2 + b^2) = 1/4 * (2) = 1/2 -> both are not equal eliminate


30-60-90

sides are in ratio 1 : sqrt(3) : 2 -> area = bh/2 = Sqrt(3)/2

1/4 * (a^2 + b^2) = 1/4 * (1 +3) = 1 -> eliminate

90-45-45

let b=h=1, area = 1/2

1/4 * (a^2 + b^2) = 1/4 * (1 + 1) = 1/2

Should be C IMO

Now sure how to check options D and E. Whats the OA?

by setting arbitrarily a=h for one side you restrict the possibilities for that side. I'd rather test by setting base freely and letting the height (h) be one-half of base (h=b/2). Then you can test opposite angle<->side relationship further and see that options d and e are not correct. For description, plz the see the pic in previous post.

shankar.ashwin wrote: Now sure how to check options D and E. Whats the OA?