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Source: — Problem Solving |

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by [email protected] » Sat Apr 19, 2014 10:30 pm
Hi shibsriz,

I'm going to give you a "nudge" and let you try this question again.

An equilateral triangle has 3 60 degree angles and 3 equal sides. By drawing a square inside of that triangle, the 3 smaller triangles take on certain characteristics. Since the 3 angles in the equilateral triangle are ALL 60s, what can you deduce about the 3 smaller triangles? Think about how triangles add up to 180 degrees and lines add up to 180 degrees. Next, think about what you know about side lengths in these triangles. You know that one of the sides is a 12; what you can figure out about the other sides?

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by theCodeToGMAT » Sun Apr 20, 2014 12:47 am
Answer = [spoiler]24 sqrt(3) + 36[/spoiler]
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by GMATGuruNY » Sun Apr 20, 2014 3:17 am
When you post a problem, please include the answer choices.
Here, the answer choices are as follows:
36
36√3
24√3 + 24
24√3 + 36
72

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CD + CE + FG = 12+12+12 = 36.

∆ADG:
On the GMAT, the perimeter of a 30-60-90 triangle will ALWAYS include √3.
Implication:
Since DG = 12, AD + AG = (something with √3).

∆BEF:
Since ∆BEF and ∆ADG are congruent, BE + BF = AD + AG = (something with √3).

Thus:
∆ABC = 36 + 2(something with √3).
Only D is viable.

The correct answer is D.
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