Thread: [SOLVED] GRE geometry problem help!

1. [SOLVED] GRE geometry problem help!

Hey guys! I came upon this problem studying for the GRE and I spent 20 minutes on it without success. I'm sure there's a long messy way to answer the question, but there should also be a simple easier way as well. Please help!

An isosceles right triangle has an area of 2x^2 + 2x + 1/2. What is the triangles perimeter?

A) 3(x+1)
B) [sqrt]2(X^2 +1)
C) (2x-1)(2x+1)
D) (2x + [sqrt]2)(2x+1)
E) 2x + [sqrt]2

Thanks folks!

2. Originally Posted by jihong
An isosceles right triangle has an area of 2x^2 + 2x + 1/2. What is the triangle's perimeter?

A) 3(x+1)
B) [sqrt]2(X^2 +1)
C) (2x-1)(2x+1)
D) (2x + [sqrt]2)(2x+1)
E) 2x + [sqrt]2
If the triangle has side s (and hypotenuse √2s) then its area is $\displaystyle A=\textstyle\frac12s^2$ and its perimeter is $\displaystyle P=(2+\sqrt2)s$. Then $\displaystyle s^2=2A=4x^2+4x+1=(2x+1)^2$. So $\displaystyle s=2x+1$ and $\displaystyle P=(2+\sqrt2)(2x+1)$. That doesn't match any of the given choices (unless there's a typo in D).