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geometry DS question

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by eclaym2003 » Sat Apr 04, 2009 8:49 am
I just got the Official Guide 12 and I am starting the data sufficiency from the back and working my way to the front. I am pleased with most of the explanations but I am stuck on a problem... here it is:

157.) The hypotenuse of a right triangle is 10cm. What is the parameter, in centimeters, of the triangle?

1.) The area of the triangle is 25 square centimeters.

2.) The 2 legs of the triangle are of equal length.

So I determined that the 2nd was sufficient enough to answer the question but I am unable to understand why the first is also sufficient. I cannot understand how you can go from xy=50 to x+y =... That's where I am having a problem. Anyway, any help would be greatly appreciated.
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Source: — Data Sufficiency |

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Re: geometry DS question

by Ian Stewart » Sat Apr 04, 2009 8:59 am
eclaym2003 wrote:I just got the Official Guide 12 and I am starting the data sufficiency from the back and working my way to the front. I am pleased with most of the explanations but I am stuck on a problem... here it is:

157.) The hypotenuse of a right triangle is 10cm. What is the parameter, in centimeters, of the triangle?

1.) The area of the triangle is 25 square centimeters.

2.) The 2 legs of the triangle are of equal length.

So I determined that the 2nd was sufficient enough to answer the question but I am unable to understand why the first is also sufficient. I cannot understand how you can go from xy=50 to x+y =... That's where I am having a problem. Anyway, any help would be greatly appreciated.
From 1, not only do we know that xy = 50; we also know that x^2 + y^2 = 100. There are a few ways to proceed from here; you could, for example, use substitution to solve. Or you might recall that we have one relationship between xy and x^2 + y^2 from factoring quadratics:

(x+y)^2 = x^2 + 2xy + y^2

And since we know x^2 + y^2 = 100, and 2xy = 100, we have:

(x+y)^2 = 100 + 100
(x+y)^2 = 200

Since x+y is positive, it must be then that x+y = root(200) = 10*root(2), and the perimeter must be 10 + 10root(2).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by mjjking » Sat Apr 04, 2009 9:05 am
Great explanation Ian, like always! :)
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by eclaym2003 » Fri Apr 10, 2009 8:42 am
OMG, thank you sooo much. I got half way through your explanation and realized where you were going. I guess I must have had a brain fart or something. Anyway, thanks again!!!
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