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In the flat triangular surface depicted above, if x = 6^1/2 feet, what

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In the flat triangular surface depicted above, if x = 6^1/2 feet, what  [#permalink]

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New post 31 Mar 2019, 08:43
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(Figure not necessarily drawn to scale.)

In the flat triangular surface depicted above, if x = \(\sqrt{6}\) feet, what is the area of the surface in square feet?

A. \(\sqrt{3}/8\)

B. \(\frac{3}{8}\)

C. \(3 \sqrt{3}/8\)

D. \(\frac{3}{4}\)

E. \(3 \sqrt{3}/4\)

Source: McGraw-Hill's GMAT

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Re: In the flat triangular surface depicted above, if x = 6^1/2 feet, what  [#permalink]

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New post 31 Mar 2019, 09:07
As you might guess seeing the √3 in the triangle, it is a 30-60-90 triangle -- the two long sides are in a √3 to 2 ratio, so the ratio of the three sides must be 1 to √3 to 2, and the shortest side must be x/2. So the area of the triangle is (1/2)(b*h) = (1/2)(x/2)(√3x/2) = √3 x^2 / 8. Since x = √6, this is equal to (√3)(√6)^2/8 = 6√3/8 = 3√3/4.
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Re: In the flat triangular surface depicted above, if x = 6^1/2 feet, what  [#permalink]

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New post 31 Mar 2019, 10:19
base of triangle can be found using Pythagorus viz.. x/2
so x= v6
area ;
1/2 * √6/2 * √6*√3/2
we get
\(3 \sqrt{3}/4\)
IMO E


SajjadAhmad wrote:
Attachment:
bhbh.jpg

(Figure not necessarily drawn to scale.)

In the flat triangular surface depicted above, if x = \(\sqrt{6}\) feet, what is the area of the surface in square feet?

A. \(\sqrt{3}/8\)

B. \(\frac{3}{8}\)

C. \(3 \sqrt{3}/8\)

D. \(\frac{3}{4}\)

E. \(3 \sqrt{3}/4\)

Source: McGraw-Hill's GMAT
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Re: In the flat triangular surface depicted above, if x = 6^1/2 feet, what   [#permalink] 31 Mar 2019, 10:19
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