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805+ Level|   Geometry|      
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In the given Figure, what is the Area of the Equilateral triangle ABC? 29 Sep 2018, 10:24
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34% (01:50) correct 66% (01:55) wrong based on 121 sessions

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Weekly Quant Quiz Question -6



In the given Figure, what is the Area of the Equilateral triangle ABC?

a) DECF is a square of area 9 cm^2.
b) BG = \(\sqrt{3}\)
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In the given Figure, what is the Area of the Equilateral triangle ABC? 29 Sep 2018, 10:32
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IMO Option (A) is correct. Please find solution in image..

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In the given Figure, what is the Area of the Equilateral triangle ABC? 29 Sep 2018, 10:30
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Answer is C as

1st Statement says :GF=3=underroot of 9
2nd statement says: BG=underroot 3

BG=CF by similar triangles...Hence both statement are sufficient to give the total length of one side and hence the area of triangle
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In the given Figure, what is the Area of the Equilateral triangle ABC? Updated on: 29 Sep 2018, 10:35
Originally posted by MikeScarn on 29 Sep 2018, 10:32.
Last edited by MikeScarn on 29 Sep 2018, 10:35, edited 1 time in total.
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Answer = A

Equilateral triangle has degree of 60 for each angle.

(1) gives us the side length of each side of the square. Now we know we have 30, 60, 90 triangles. Other measures can be determined to find the area.

Sufficient
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In the given Figure, what is the Area of the Equilateral triangle ABC? 29 Sep 2018, 10:33
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1) sufficient
since DBG forms a triangle of 30-60-90
BG=root 3
GF=3
FC=root 3 again we got the base
with same process we can get the height of the triangle
no need to find that out. sufficient
2) BG=root 3
we can get the length of DG by same process as used in first
and if will get the base of the triangle, we can get the height as well
sufficient
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In the given Figure, what is the Area of the Equilateral triangle ABC? 29 Sep 2018, 10:37
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If ABC is equilateral triangle, the side of square which bisects the two sides other than base will be half of the base.

Consider A, side of DECF = 3. Base/ any side of equilateral triangle is 6. Area = \sqrt{3}/4 *6*6 = 9\sqrt{3}. A is sufficient.

Consider B, only BG is known. Nothing else is given. Triangle can be any type. So it is not sufficient.

Answer A.
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In the given Figure, what is the Area of the Equilateral triangle ABC? 29 Sep 2018, 10:43
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1. Suff........ we know DG=3 & angle b = 60 ...we can determine BG and thus BC and thus areaABC.
2. NS .........if BG = root3.... we donot have a way to determine any side of triangleABC...... Ans A
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In the given Figure, what is the Area of the Equilateral triangle ABC? 29 Sep 2018, 12:21
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Ans. A

As area of square is 9, side of square= height of 2 smaller triangles = 3

As the triangle is equilateral, angle B and angle C = 60 degree. Angle G and angle F = 90 (given as it’s a square)

Thus angle BDG and angle CEF =30 degree.
Using 30-60-90 property of triangle, we can find out sides BG and CF. Thus, we will have BC=BG + GF + FC

One side of the triangle BC is sufficient to find area of the equilateral triangle ABC

Hence, A is sufficient

B) BG is given. However, we have no idea about GF or any other side. Thus not sufficient.

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In the given Figure, what is the Area of the Equilateral triangle ABC? 02 Aug 2022, 15:56
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