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.