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Geometry mystery! OG 11 - Quant Review(green) DS#109

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Geometry mystery! OG 11 - Quant Review(green) DS#109

by alex.gmat » Tue Jul 14, 2009 4:51 pm
Hello all!
I am seeking your expert advice on a problem that confuses me. Thank you in advance!

We are given a rectangular region with length l , width w, and diagonal d

What is the area of the rectangular region?

1. l + w = 6
2. d^2 = 20


The OA confuses me greatly! In particular, why the Pythagorean theorem cannot be used to solve the problem, since it is true that for every rectangle D = sqrt (x^2 + y^2) and that a diagonal in a rectangle divides it into two identical 30-60-90 triangles??

Thank you again for your input!

Alex
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Re: Geometry mystery! OG 11 - Quant Review(green) DS#109

by Ian Stewart » Tue Jul 14, 2009 5:38 pm
alex.gmat wrote:
The OA confuses me greatly! In particular, why the Pythagorean theorem cannot be used to solve the problem, since it is true that for every rectangle D = sqrt (x^2 + y^2) and that a diagonal in a rectangle divides it into two identical 30-60-90 triangles??
The diagonal of a rectangle does not normally divide the rectangle into two 30-60-90 triangles. In fact, that will only happen if the ratio of the length to the width is equal to root(3) to 1. If you think of a square (which is a rectangle), for example, the diagonal divides it into two 45-45-90 triangles.
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by alex.gmat » Tue Jul 14, 2009 9:00 pm
Thank you for the reply!
My bad on the 30-60-90 statement - your clarification totally makes sense; however, does d=sqrt(x^2 + y^2) still hold true for any rectangle? If it does, why can't we use this with statement (2) to solve the problem?

Thank you again!
I just wanted to say how helpful this forum has been in the process of my preparation for the GMAT. To everyone involved - you rock!

A.
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My answer for the above question...

by struggling_guy2001 » Tue Jul 14, 2009 9:51 pm
I strongly feel that both the statements are required and enough to solve the problem.

Use the Phythagoras theorem

i.e.

(Length) ^2 + ( Breadth ) ^2 = ( Diagonal )^2.

By solving the equation. we get L= 2 or 4 and B = 4 or 2.

Hence the are would be 8 sq.units in both the cases.

Hence I would go for the option Both the statements are enough and required to solve the problem.
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