Question 879730: Area of a equilateral triangle is 24 root 3 cm square . Then what will be its perimeter ?
Answer by harpazo(655)   (Show Source):
You can put this solution on YOUR website! The area of an equilateral triangle is found using the formula
A = (a^2)*sqrt(3)/4.
You were given the area to be 24sqrt(3)cm.
The perimeter of this particular triangle is found using the formula P = 3a, where a is the side length of the triangle.
Go back to the area formula, replace A with 24*sqrt(3) and solve for a as your first step.
24*sqrt(3) = (a^2)*sqrt(3)/4
4*24*sqrt(3) = (a^2)*sqrt(3)
We are solving for a. This is our goal.
96*sqrt(3) = (a^2)*sqrt(3)
96*sqrt(3) divided by sqrt(3) = a^2
96 = a^2
We now take the square root of both sides.
sqrt(96) = sqrt(a^2)
sqrt(16)*sqrt(6) = a
4*sqrt(6) = a.
Now that we know the value of a, we plug that into the perimeter formula to find the perimeter of the triangle.
P = 3a
P = 3(4*sqrt(6))
P = 12*sqrt(6) cm.
Did you follow?
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