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26 May 2007, 15:45
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A Square is inscribed in an equliateral triangle. If an edge of the square = 12 then what is the perimeter of the equilateral triangle.
A 36
B 36sqrt3
C 36sqrt3+24
D 24sqrt3+26
E 72
This was from an 800 score test. I am not 100% clear on part two of their explanation which is way down below. I have a bunch of questions down there if someone would be so kind and explain the answers to me.
step two of their explanation is that the triangle on top of the square is also equilateral because it is similar to the larger triangle. How do I know if triangle's are similar? (and what exactly does that mean?)
what is the proof of similarity in this situation? I need to prove something before I can understand it. How do I test for similarity in other situations? what are sufficient and necessary conditions for similarity? If I knew that part everything else would have come naturally. Thanks
A 36
B 36sqrt3
C 36sqrt3+24
D 24sqrt3+26
E 72
This was from an 800 score test. I am not 100% clear on part two of their explanation which is way down below. I have a bunch of questions down there if someone would be so kind and explain the answers to me.
step two of their explanation is that the triangle on top of the square is also equilateral because it is similar to the larger triangle. How do I know if triangle's are similar? (and what exactly does that mean?)
what is the proof of similarity in this situation? I need to prove something before I can understand it. How do I test for similarity in other situations? what are sufficient and necessary conditions for similarity? If I knew that part everything else would have come naturally. Thanks
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26 May 2007, 18:24
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gmatiscoming
Three triangles are formed when the square is inscribed inside the equilateral triangle. Two are on the bottm ( left and right flange ) and one on the top. The bottm ones have two angles as 60degrees and 90degrees ( because square has 90degrees ). Therefore the third angle is 30degrees. Thus you can easily see that the angles of the top triangle are 60degrees each and thus equilateral. Rest follows....... Does that make it clear to you?
Please look in termas of angles of the three triangles formed and you will see that the top one is equilateral.
