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

Question

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} gmatbusters Quiz.jpeg

saukrit · Answer

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

Gladiator59 · Answer

IMO Option (A) is correct. Please find solution in image..

Gladi

MikeScarn · Answer

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

Manvi_nagpal · Answer

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

akshaykotha · Answer

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.

u1983 · Answer

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

mongmat27 · Answer

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.

Posted from my mobile device

bumpbot · Answer

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

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