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# In the figure above, the area of ∆ ABC is 32, and the total area of

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
In the figure above, the area of ∆ ABC is 32, and the total area of  [#permalink]

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06 Nov 2017, 21:56
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Difficulty:

25% (medium)

Question Stats:

89% (01:05) correct 11% (01:15) wrong based on 32 sessions

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In the figure above, the area of ∆ ABC is 32, and the total area of the three smaller triangles is 16. If DEFG is a square, what is the length of segment GF?

(A) 4
(B) 5
(C) √34
(D) 6
(E) 5√2

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2017-11-07_0941_002.png [ 6.03 KiB | Viewed 577 times ]

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In the figure above, the area of ∆ ABC is 32, and the total area of  [#permalink]

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06 Nov 2017, 23:52
1

From the figure, we know that the area of the triangle(ABC) is 32.
It has also been given that the sum of the other smaller triangles is 16.

Therefore the figure DEFG has to be having area of 16(which is a square)
Since the segment(GF) is the side of the square DEFG,
the length must be $$\sqrt{16}$$ or $$4$$(Option A)
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Re: In the figure above, the area of ∆ ABC is 32, and the total area of  [#permalink]

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10 Nov 2017, 08:40
Area of square = Area of ABC - area of three mall triangle.
GF^2 = 32-16 = 16
GF =4.
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Re: In the figure above, the area of ∆ ABC is 32, and the total area of &nbs [#permalink] 10 Nov 2017, 08:40
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