Simple Geometry Problem

[student22]

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?

[GMAT680]

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

[student22]

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.

[akahuja143]

No assumptions on DS questions!!

[student22]

I know, I know, I try to catch myself whenever I make assumptions on DS.