Equilateral triangle has area of 9 times the square root of 3 inches. How many inches is perimeter?
let each side be x inches
Area = (1/2)(x)(x)sin60° = 9√3
(1/2)(x^2)√3/2 = 9√3
x^2 = 36
x = 6
perimeter = 3x = 18
To find the perimeter of an equilateral triangle, we need to know the length of its sides.
In this case, we are given the area of the equilateral triangle as 9 times the square root of 3 square inches. However, we cannot directly calculate the length of the sides from the area alone.
To find the length of the sides, we need to use the formula for the area of an equilateral triangle. The formula is A = (sqrt(3) / 4) * s^2, where A is the area and s is the length of each side.
In this case, we have the area A = 9*sqrt(3), so we can rewrite the formula as 9*sqrt(3) = (sqrt(3) / 4) * s^2.
To solve for s, we can rearrange the equation: s^2 = (4 * 9 * sqrt(3)) / sqrt(3).
Simplifying further, s^2 = 36, which gives us s = 6.
Now that we know the length of one side is 6 inches, we can find the perimeter by multiplying the length of one side by the number of sides in the equilateral triangle. Since an equilateral triangle has 3 sides, the perimeter is 6 * 3 inches = 18 inches.
Therefore, the perimeter of the equilateral triangle is 18 inches.