Question

tovaru
12. Find the perimeter of an equilateral triangle having area 16v3 cm2.
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Answer 1

Solution :-

Let the side of the equilateral triangle be 'a 'cm

Area of the equilateral triangle = 16√3 cm²

Also, Area of a equilateral triangle = √3 * a² / 4 sq. units

[ Where a is the side of the equilateral triangle ]

⇒ 16√3 = √3 * a² / 4

⇒ 16√3 / √3 = a² / 4

⇒ 16 = a² / 4

⇒ 16 * 4 = a²

⇒ 64 = a²

⇒ √64 = a

⇒ ± 8 = a

Sides cannot be negative

⇒ a = 8

Perimeter of an equilateral triangle = 3a units

[ Where a is the side of an equilateral triangle ]

= 3 * 8 = 24 cm

Therefore the perimeter of an equilateral triangle is 24 cm.