An equilateral triangle has the area of 25 squared root of 3 squared. What is the height? Round answer to the one decimal place.
I can only guess what this means :
area of 25 squared root of 3 squared
A = (1/2) b h
tan 60 = h/(b/2) = sqrt 3
so b/2 = h / sqrt 3
25 sqrt 3 = (h/sqrt 3)h = h^2/sqrt 3
h^2 = 25*3
h = 5 sqrt 3
8.7
To find the height of an equilateral triangle, we can use the formula:
Height = (√3/2) * Side
We are given that the area of the equilateral triangle is 25√3^2 (square units).
The formula for the area of an equilateral triangle is:
Area = (√3/4) * Side^2
Let's use this formula to find the length of the side of the equilateral triangle:
25√3^2 = (√3/4) * Side^2
Multiplying both sides by 4/√3:
(25√3^2) * (4/√3) = Side^2
100√3 = Side^2
Now, let's take the square root of both sides to find the length of the side:
√(100√3) = Side
Simplifying √(100√3):
√(100 * √3) = Side
√300 = Side
Since an equilateral triangle has all sides equal, the length of one side is √300.
Now, let's substitute this value into the formula for the height:
Height = (√3/2) * Side
Height = (√3/2) * √300
Height = (√3/2) * √(100 * 3)
Height = (√3/2) * 10√3
Height = (10√3 * √3) / 2
Height = (10 * 3) / 2
Height = 15 / 2
Height ≈ 7.5 (rounded to one decimal place)
Therefore, the height of the equilateral triangle is approximately 7.5 units.