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If the length of the side of the inscribed square measures 12 inches,

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Sloan MIT School Moderator
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If the length of the side of the inscribed square measures 12 inches,  [#permalink]

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New post 22 May 2020, 10:11
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A
B
C
D
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Difficulty:

  55% (hard)

Question Stats:

56% (02:04) correct 44% (01:55) wrong based on 24 sessions

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If the length of the side of the inscribed square measures 12 inches, what is the area of triangle ABC?

1) ABC is an equilateral triangle
2) The height o the triangle ABC from point C is \(6\sqrt{3}+12\)

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Re: If the length of the side of the inscribed square measures 12 inches,  [#permalink]

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New post 22 May 2020, 17:13
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Statement 1-

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Triangle GAD and FBE are (30-60-90) triangles. Hence, we can find AD and EB

We can find AB = AD+DE+EB.

Hence, we can find area of ABC (\(\frac{√3*(AB)^2}{4}\))

Sufficient.

Statement 2-

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Triangle CGF is similar to CAB.

\(\frac{CH}{CI} = \frac{GF}{AB}\)

Since we know CH, CI and GF, We can find AB.

Area = \(\frac{1}{2} *CI * AB\) (We know AB and CI)

Sufficient
GMAT Club Bot
Re: If the length of the side of the inscribed square measures 12 inches,   [#permalink] 22 May 2020, 17:13

If the length of the side of the inscribed square measures 12 inches,

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