What is the area of equilateral triangle ABC?

Question

(1) Side AB measures 12 meters in length.

(2) The shortest distance from side AB to angle ACB is 6√3 meters.

Kudos for a correct  solution .

chetan2u · Answer

ans D..
1) sufficient.. straight from area formulae when side is known
 2)sufficient.. the shortest dist is nothing but altitude from which side can be found and then area formulae can be used..

Icerockboom · Answer

Can anybody help me clarify "the shortest distant" and the altitude?

chetan2u · Answer

hi.... the shortest distance from a vertex/a point to a line is always a perpendicular distance of that point from that line...
 and this perpindicular distance is nothing but the altitude...

Icerockboom · Answer

Then, the answer must be C. As we have known a side and a altitude for that side.

EMPOWERgmatRichC · Answer

Hi Icerockboom,

The correct answer is actually  D  and here's how you can prove it:

1) Draw an equilateral triangle
2) Fill in the values for the angles and the sides that you're given.
3) Draw a line right down the middle (cut the triangle "in half") and form 2 smaller triangles. What kind of triangles have you just formed?
4) Using those smaller triangles, can you figure out the "base" and the "height"
5) When you have those values, you can figure out the area of the triangle.

GMAT assassins aren't born, they're made,
Rich

smartyguy · Answer

What is the area of equilateral triangle ABC?

(1) Side AB measures 12 meters in length.

As it is given equilateral triangle so the area will be √3/4*s^2
so here AB side is given hence sufficient.

(2) The shortest distance from side AB to angle ACB is 6√3 meters.

As shortest distance is 6√3 given so it will make an angel of 90degrees on AB as it is perpendicular.
Moreover it is mentioned that the triangle is equilateral so angle b is 60 therefore 30-60-90 by this we can know the side.
hence sufficient.

Ans D

Regards
SG

chetan2u · Answer

hi.. you dont require both side and altitude. both are interdependent in an equilateral triangle. if u know side say'a', the altitude will be \sqrt{3}a/2..
 as u draw an altitude in the equilateral triangle, side is 'a', which becomes hypotenuse. the base is a/2.. so the altitude or perpendicular is a^2-(a/2)^2= \sqrt{3}a/2

peachfuzz · Answer

Each angle of an equilateral triangle is 60 degrees. Based off of that, we know that if we were to split the triangle in half by two, this would give us a 30-60-90 triangle with the ratios of 1x : 2x : x√3

Statement 1: Side AB is 12. that means the area is equal to 2*(1/2)(6)(6√3 ). Sufficient.

Statement 2: This is the altitude of the equilateral triangle. 6√3 (height) tells us that one side of the equilateral triangle is equal to 12. Area is equal to 2*(1/2)(6)(6√3 ).

Answer: D

Cadaver · Answer

D....

A - Side known , direct formula (3)^1/2/4 a^2 for area.

B - Altitude known, apply Tan 60 in the small triangle formed. get side. get area

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION: Because equilateral triangles are perfectly symmetrical, typically one known piece of "length" information (whether it's a side length, perimeter, or area) will tell you all the other dimensions. In this case, knowing one side allows you to use the principles of 30-60-90 triangles to find the height. The perpendicular line from angle C down to side AB will divide the triangle into two identical 30-60-90 triangles each with a hypotenuse of one complete side and dimensions as shown below: equilateral.png So in this case, each statement alone is sufficient, as each will plug in one side of the 30-60-90 triangles in the above diagram, allowing you to fill in for the rest and solve for the area. The answer is D.

rhine29388 · Answer

Statement 1 gives side of triangle from which we can easily find area of equilateral triangle
Statement 2 gives us information on actually the height of the triangle from which bt using 30 - 60 - 90 triangle properties we can easily find area of equilateral triangle
Hence correct answer - D

What is the area of equilateral triangle ABC?

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What is the area of equilateral triangle ABC?

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