An equilateral triangle has an area of 25 √3 cm squared. what is the height

Height = 8.66 cm

Step-by-step explanation:

The formula for the area of an equilateral triangle is expressed as

A = S²√3/4,

where s represents the length of each side. The area of the given equilateral triangle is 25 √3 cm squared. Therefore

25 √3 = S²√3/4

Dividing both sides of the equation by √3, it becomes

25 √3/√3 = S²√3/4√3

25 = S²/4

Cross multiplying, it becomes

S² = 25 * 4 = 100

Taking square root of both sides of the equation, it becomes

√S² = √ 100

S = 10 cm

In an equilateral triangle, all the sides are equal. The height of the equilateral triangle divides it into two equal right angles triangle. The angles in each right angle triangle are 90, 60 and 30 degrees. To determine the height, h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

10² = h² + 5²

100 = h² + 25

h² = 100 - 25 = 75

h = √75

h = 8.66 cm

5 √ 3 c m

A t = √ 34 * s 2 = 25 √ 3

this makes the sides 10cm

At = 1/2 b * h

25 √ 3 = 12 ⋅ 10 ⋅ h = 5 √ 3 c m