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Geometry Strategies - Triangle and Square

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by gmattesttaker2 » Sat Aug 11, 2012 10:29 pm
Hello,

This is from MGMAT Geometry Strategy Guide:

The side of an equilateral triangle has the same length as the diagonal of a square. What is the area of the square?

1) The height of the equilateral triangle is equal to 6root3
2) The area of the equilateral triangle is equal to 36root3

OA: D

I am clear with 1) but not with 2). Can you please explain? Thanks a lot.

Best Regards,
Sri
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by niketdoshi123 » Sat Aug 11, 2012 11:44 pm
gmattesttaker2 wrote:Hello,

This is from MGMAT Geometry Strategy Guide:

The side of an equilateral triangle has the same length as the diagonal of a square. What is the area of the square?

1) The height of the equilateral triangle is equal to 6root3
2) The area of the equilateral triangle is equal to 36root3

OA: D

I am clear with 1) but not with 2). Can you please explain? Thanks a lot.

Best Regards,
Sri
Statement 2:
Area of equilateral triangle = √3/4 *s², where s is the length of the side of the triangle.
36√3 = √3/4 * s²
=> s = 12 = diagonal of the rectangle
Hence you can find the area of the rectangle
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by gmattesttaker2 » Sun Aug 12, 2012 7:12 pm
niketdoshi123 wrote:
gmattesttaker2 wrote:Hello,

This is from MGMAT Geometry Strategy Guide:

The side of an equilateral triangle has the same length as the diagonal of a square. What is the area of the square?

1) The height of the equilateral triangle is equal to 6root3
2) The area of the equilateral triangle is equal to 36root3

OA: D

I am clear with 1) but not with 2). Can you please explain? Thanks a lot.

Best Regards,
Sri
Statement 2:
Area of equilateral triangle = √3/4 *s², where s is the length of the side of the triangle.
36√3 = √3/4 * s²
=> s = 12 = diagonal of the rectangle
Hence you can find the area of the rectangle
Hi Niket,

Thanks for your explanation. It is clear now.

Best Regards,
Sri
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