Answer:
6√24 or 29.39metres
Explanation:
Area of a triangle is bh/2
The perimeter of an equilateral triangle is 3b
This equilateral triangle can be imagined as two adjoining 30-60-90 triangles. Together, their area is the given 24√3 m²
The base of the individual triangle is √24. The height is √24√3. Multiplying those factors, we get the given area, a proof of sorts, but mure importantly, we can calculate the length of the hypotenuse as 2√24.
sin(30°) = 0.5
√24/(0.5) = 2√24
That is the length of the side of the original equilateral triangle.
The perimeter is 3 times the length of the side:
(3)(2√24) = P
6√24 meters is the perimeter.