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

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Joined: 07 Mar 2019
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Location: India
GMAT 1: 580 Q43 V27
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If the length of the side of the inscribed square measures 12 inches,  [#permalink]

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22 May 2020, 10:11
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Difficulty:

55% (hard)

Question Stats:

50% (02:11) correct 50% (01:56) wrong based on 15 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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GMATPREP1 590(Q48,V23) March 6, 2019
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Re: If the length of the side of the inscribed square measures 12 inches,  [#permalink]

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22 May 2020, 17:13
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1
Statement 1-

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Untitled.png [ 9.06 KiB | Viewed 140 times ]
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-

Attachment:

Untitled.png [ 6.49 KiB | Viewed 140 times ]
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
Re: If the length of the side of the inscribed square measures 12 inches,   [#permalink] 22 May 2020, 17:13