If the perimeter of an equilateral triangle is 60 cm, then what is its area? a. 200√2cm2 b. 100√2cm2 c. 100√3cm2 d. 200√3cm2
Question
If the perimeter of an equilateral triangle is 60 cm, then what is its area?
a. 200√2cm²
b. 100√2cm²
c. 100√3cm²
d. 200√3cm²
Solution
The perimeter of an equilateral triangle is the sum of the lengths of all its sides. Given that the perimeter is 60 cm, and knowing that all sides of an equilateral triangle are equal, each side measures 60/3 = 20 cm.
The formula to calculate the area (A) of an equilateral triangle given the length of its side (a) is: A = (a² * √3) / 4.
Substituting the value of a (20 cm) into the formula, we get: A = (20² * √3) / 4 = 100√3 cm².
Therefore, the area of the equilateral triangle is 100√3 cm², which corresponds to option c.
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