Recalling that the area of a triangle of base b and height h is (1/2)(base)(height),
we equate this formula to the given area, 9√3, of this equilateral triangle:
(1/2)(base)(height) = 9√3.
Now, if the base of the triangle is b, then the height is b*sin (60 degrees), or
b*√3/2. Reworking the formula given above,
(1/2)(b)(√3*b/2) = 9√3
Simplify this by dividing both sides by √3:
b^2
------- = 9, or b^2 = 36, or b = 6
4
The equilateral triangle has side length 6 (i. e., all three sides are of length 6).
