Simple Geometry Problem

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student22: Master | Next Rank: 500 Posts; Posts: 216; Joined: Mon Dec 21, 2009 10:26 am; Thanked: 16 times

Simple Geometry Problem

by student22 » Fri Mar 26, 2010 4:57 pm

Everywhere I've seen this problem the answer is C. How come it's not b?

What is the area of the rectangular region above?

(1) L+W = 6
(2) D^2 = 20

I thought the rule was that a diagonal turns a rectangle into 2 30-60-90 triangles. So D = sqrt(20), therefore W = sqrt(20)/2 and L = sqrt(20)/2 * sqrt(3). What am I missing?

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Source: Beat The GMAT — Data Sufficiency | Fri Mar 26, 2010 4:57 pm

GMAT680: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Wed Feb 17, 2010 6:15 pm; Location: MD; Thanked: 2 times

by GMAT680 » Fri Mar 26, 2010 6:11 pm

Student 22,

I think the problem with your solution is your assumption of 30-60-90 triangle. You do not have enough information to assume so. if the 4 sided polygon was a square it is 45-45-90. As the length of one side vary the angles vary as well. But statement 1 and 2 combined will solve the problem.

Hope this helps

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student22: Master | Next Rank: 500 Posts; Posts: 216; Joined: Mon Dec 21, 2009 10:26 am; Thanked: 16 times

by student22 » Fri Mar 26, 2010 7:08 pm

Hmmm....I thought that there was only one way to cut a rectangle with a diagonal line, but now that I think about it you're absolutely right.

A square is a type of rectangle so logically if a square could be cut into a 45-45-90 triangle, then a rectangle does not have to be a 30-60-90.