Find the attachment. I tried adding the image in the post;

Question

Find the attachment. I tried adding the image in the post; however, all in vain. So, attached the complete question. 1.jpg

gurpreetsingh · Answer

Statement 1 : Not sufficient.
We know the position of B, but not the position of A. Thus we can not calculate the value of AB.

Statement 2: Sufficient.
We know the position of C 
=> we know the perpendicular distance from the line AB
=> we know the altitude of the triangle
=> we have the area.

Hence the Answer is B.

fluke · Answer

Area_Of_Equilateral_triangle.PNG (1) A can be (0, 0.000000000001) Or A can be (0, 5) Both resulting in different area for ABC. Not Sufficient. (2) We know the altitude of the triangle. Distance between y-axis and coordinate C or 6. Thus, the area can be found. Altitude=\frac{\sqrt{3}}{2}*(Side)=6 Area = \frac{\sqrt{3}}{4}(side)^2 Sufficient. Ans: "B"

jamifahad · Answer

Stmt1 . We know only one co-ordinate. we don't know altitude, base or one side of triangle. Hence insufficient.

Stmt2: We know altitude when draw from C to opposite base is 6. Also this altitude will bisect the angle ACB making each angle 30.
So cos30 = altitude/CA {imagine a line from C to AB}
 \sqrt{3}/2=6/CA

CA= 12/\sqrt{3}.  We know one side of EQUILATERAL triangle.

Apply formula Area of equilateral triangle= s^2 * \sqrt{3}/4
= (12/\sqrt{3})^2* \sqrt{3}/4
= 12\sqrt{3} 
Hence sufficient.

OA B.

fluke · Answer

I know it doesn't change the answer. But, is it sin{30} or cos{30}?

jamifahad · Answer

oh yes cos30. i was timing my solution. got mixed up. thanks.

amit2k9 · Answer

a the distance from origin to A is not known.Hence side of the equilateral triangle cannot be calculated. Not sufficient.

b C has x coordinate = 6 = altitude of equilateral triangle 
 y coordinate = 3* 3^(1/2) also does not account for the distance from origin to A.

however altitude a = 6 means side = 6*2/3^(1/2) as in a triangle with angle 60 deg sides are in the ratio 3^(1/2)(perpendicular):1 (base):2(hypotenuse)

thus area can be calculated.

B

pkmme · Answer

Thanks guys, indeed the OA is B.

hussi9 · Answer

Yup B is sufficient

With point C there is only one possible equilateral triangle. Hence we can find it area

subhashghosh · Answer

(1)
Let Co-ord of A = (0,y)

5root(3) - y = Side

Insufficient

(2)

A median drawn from C will bisect AB

and there will be 30-60-90 triangle

The length of perpendicular is known

so other sides can be found, and this the area can be found

Sufficient

Answer - B

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