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Math Help - [SOLVED] GRE geometry problem help!

  1. #1
    jihong
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    [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!
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Quote Originally Posted by jihong View Post
    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 A=\textstyle\frac12s^2 and its perimeter is P=(2+\sqrt2)s. Then s^2=2A=4x^2+4x+1=(2x+1)^2. So s=2x+1 and P=(2+\sqrt2)(2x+1). That doesn't match any of the given choices (unless there's a typo in D).
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