Geometry

[swerve]

In the figure above, segments \(AB\) and \(CD\) represent two different ways the same steel girder can support wall \(EC.\) The length of \(AE\) is how much greater than the length \(DE?\)

1. The length of \(AB\) is \(20\) meters

2. The length of \(DE\) is \(8\) meters

The OA is D

[gmatter2012]

2015-01-14_1320.png

In the figure above, segments \(AB\) and \(CD\) represent two different ways the same steel girder can support wall \(EC.\) The length of \(AE\) is how much greater than the length \(DE?\)

1. The length of \(AB\) is \(20\) meters

2. The length of \(DE\) is \(8\) meters

The OA is D

Please post the explanation, how is the answer D and NOT C. Thank you in advance.

[beatthegmat]

Hello,

The key to this question is that the lengths of AB and CD are the same (we're told that they are the same steel girder). Since the two triangles are a 45/45/90 and a 30/60/90, if we are given the lengths of any side of either triangle, then we can figure out the other sides of that triangle and then figure out all of the sides of the second triangle. Statement 1 and statement 2 each give us one of the lengths, so each statement is sufficient on its own to answer the question.