.If the area of an equilateral triangle is 9√3 cm2
, find its side
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Answer:
The area of any triangle is (1/2)ba, where b is the length of the base and a is the height of the altitude of the triangle.
In every equilateral triangle the altitude will be equal to (√3)b/2.
Substitute these values into the triangle area formula 1/2ba
(1/2)(b) x (√3)b/2 = 9√3 cm² : Multiply both sides by 4 to clear the fractions.
√3b² = 36√3 cm² : divide both sides by √3 to isolate b²
b² = 36 cm² : take the square root of both sides to isolate b
b = 6 cm : simplify the radical
So each side is 6 cm
The perimeter is the sum of all three sides: 6 cm + 6 cm + 6 cm = 18 cm.
The perimeter is 18 cm.
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