The area of an equilateral triangle is $\sqrt{3}$. What is the perimeter of the triangle?

Question

Prepp Team · Accepted Answer

Finding Equilateral Triangle Perimeter

The problem asks for the perimeter of an equilateral triangle given its area.

Area Formula: The area ($A$) of an equilateral triangle with side length ($s$) is given by the formula: $A = \frac{s^2 \sqrt{3}}{4}$
Given Area: We are given that the area $A = \sqrt{3}$.
Calculate Side Length ($s$): Substitute the given area into the formula and solve for $s$: $ \sqrt{3} = \frac{s^2 \sqrt{3}}{4} $ Divide both sides by $\sqrt{3}$: $ 1 = \frac{s^2}{4} $ Multiply both sides by 4: $ s^2 = 4 $ Take the square root of both sides (since side length must be positive): $ s = \sqrt{4} = 2 $ So, the side length of the equilateral triangle is 2.
Calculate Perimeter: The perimeter ($P$) of an equilateral triangle is 3 times its side length ($s$): $ P = 3s $ Substitute the calculated side length ($s=2$): $ P = 3 \times 2 = 6 $

Therefore, the perimeter of the equilateral triangle is 6.

Prepp Team · Answer

2

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4

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8