Geometry question

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Kazuyac: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Thu Mar 31, 2011 5:28 pm

Geometry question

by Kazuyac » Thu Mar 31, 2011 5:44 pm

Hi all,

I'm currently studying the Manhattan GMAT's "Geometry" strategy guide and came across a 2nd chapter practice question that's been stumping me. It involves finding the area of an Isoceles right triangle. Was hoping somebody could help me out:

"6.The longest side of an Isosceles right triangle measures 20-square root of 2. What is the area of the triangle?"

Thanks in advance.

Quote

Source: Beat The GMAT — GMAT Strategy | Thu Mar 31, 2011 5:44 pm

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 am; Thanked: 156 times; Followed by:34 members; GMAT Score:720

by vineeshp » Thu Mar 31, 2011 6:14 pm

Hey.

"Longest side of an isosceles right triangle." is your key.

First property to use: Right triangle means that if three sides are of length a, b and c with c the length of the side opposite to the right angle, we know 2 things. c is the longest side and
c^2 = a^2 + b^2.

Second property: If you have a right triangle, you can find the area of the triangle if you know the length of the two sides that hold the right angle. area of our triangle is (1/2)*a*b

Now in the case of an isosceles right triangle, 2 sides are equal. So in this case we have a and b are equal. b and c cannot be equal. a and c also cannot be equal. This is because c is the length of the hypotenuse and has to be the longest side. Right?
And area is (1/2)*a*a

So in this question we have a=b
Applying this in
c^2 = a^2 + b^2 = c^2 = a^2 + a^2
This can help us find the value of a as c is given.

Now area is (1/2) a^2.

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