Respuesta :
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
Answer:
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
