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

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

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31 Mar 2019, 08:43
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25% (medium)

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81% (01:44) correct 19% (03:19) wrong based on 21 sessions

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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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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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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

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
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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