Posted by **jenny** on Wednesday, May 4, 2011 at 6:48am.

The area of an equilatoral triangle ABC is 50cm^2 . Find AB.

- maths (mensuration) -
**Reiny**, Wednesday, May 4, 2011 at 7:04am
We know all angles are 60° and all sides are equal.

Let the side be x cm

(1/2)(x)(x)sin60° = 50

x^2 = 100/(√3/2) = 200/√3

x = 10√2/(√√3)) = appr. 10.75 cm

or let each side be 2x

then the height is √3 x

area = (1/2)(2x)(√3x) = 50

√3x^2 = 50

x^2 = 50/√3

x = 5.3728 appr.

so 2x, the side is appr. 10.75

- maths (mensuration) -
**drwls**, Wednesday, May 4, 2011 at 7:04am
Area = (1/2)*base*(base/2)*sqrt3

= (sqrt3)(base)^2/4 = 50

base^2 = 200/sqrt3 = 115.47

base = 10.7456599

All sides have that length, since the triangle is equilateral.

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