what is the perimeter of an equilateral triangle whose area is 25 sqrt3?

Question

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Answer 1

Area of triangle = 1/2 * b * h. The base (b) is the length of each side of the equilateral triangle. In an equilateral triangle, the height (h) is found from Pythagoras' Theorem as:

h^2 + (b/2)^2 = b^2
h = sqrt(b^2 - (b/2)^2)

Solving for b using the given area should give us the length of each of the sides for the equilateral triangle:

25 sqrt(3) = 1/2 * b * sqrt(b^2 - (b/2)^2)
50 sqrt(3) = b sqrt(b^2 - (b^2)/4) ....after multiplying by 2
2500 * 3 = b^2 * (b^2 - (b^2)/4) ....after squaring both sides
7500 = b^2 * 3/4 b^2
10000 = b^4
b = 10

Perimeter of equilateral triangle = 3 * b = 30

Answer 2

A = bh/2 = 25sqrt3. It's pretty obvious that bh = 50sqrt3. Since the triangle is equilateral, the height is sqrt3/2 times the base. So h = bsqrt3/2. bh = b^2 sqrt(3)/2 = 50sqrt(3). Solving for b, b = 10. Since P = 3b, the perimeter = 30.

Answer 3

P = 3a
A = (a^2 * sqrt(3))/4

25sqrt(3) = (a^2 * sqrt(3))/4
100sqrt(3) = a^2 * sqrt(3)
a^2 = 100
a = 10

P = 3(10)
P = 30

ANS : 30