Question

An equilateral triangle has a perimeter of 90 inches. Find the area of the equilateral triangle, I simplest form.

Answer 1

389.7 square inches

Explanation:

equilateral triangle = each side has the same lenght

90 inches / 3 = 30 inches each side

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Pythagoras

30^2 = 15^2 + x^2

900 - 225 = x^2

v 675 = x

25.98 = x

x = height

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Area = BxH/2

B = 30 inches

H = 25.98

(30 x 25.98) /2 = 389.7 square inches

Answer 2

390 in²

Explanation:

Length of the sides of the triangle = 90/3 = 30 in

area of a triangle = (base × height)/2

height of an equilateral triangle with sides of length x
`=(√(3) )/(2)x`

Then the height of our triangle
`=(√(3) )/(2) *30=26`

Conclusion:

area of the triangle = (30 × 26)/2 = 390 in²