Question

find the perimeter of an equilateral triangle whose area is 24√3m²
please give step by step explanation​

Answer 1

Answer: Perimeter = 12√6 m.

Explanation:

Area of an equilateral triangle = (√3)/4 × x^2

Given that, area = (24√3) m^2

Therefore, (√3)/4 × x^2 = 24√3

⇒ x^2/4 = 24

⇒ x^2 = 24 × 4

⇒ x = √(24 × 4) = 4√6.

So, Perimeter = 3x = 3(4√6) = 12√6 m.

Answer 2

area of equilateral triangle = √3/4 a²

where a = side of triangle

so,

√3/4 a² = 24√3

√3 on both side will get cancel and shift 1/4 on r.h.s.

a² = 24 × 4

a. = √24×4

a = 2×2×{√2×3}

a = 4 √6

so , perimeter = 3a or a + a + a

= 12√6

hope this helps you

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