Question

Q.18 If area of equilateral triangle is 16V3 sq. cm., then its perimeter is cm a)24 b) 48 c)12 d)36
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Answer 1

Required Answer :

The perimeter of the equilateral triangle = 24 cm

Option → a) 24 cm

Given :

• Area of equilateral triangle = 16√3 cm²

To find :

• Periemeter of the equilateral triangle

Solution :

In this question, we are given the area of an equilateral triangle and we need to calculate the perimeter. So, firstly we will calculate the side of the equilateral triangle by using the formula of the area of equilateral triangle itself. And then after getting its value we will apply the required values in the formula of perimeter of equilareral triangle to get the required answer.

Using formula,

• Area of equilateral triangle = √3/4 a²

where,

• a denotes the side of the triangle

Substituting the given values :

⇒ 16√3 = √3/4 a²

⇒ 16√3 × 4/√3 = a²

⇒ 16 × 4 = a²

⇒ 64 = a²

⇒ Taking square root on both the sides :

⇒ √64 = a

⇒ √(8 × 8) = a

⇒ ± 8 = a

As we know, the side of triangle cannot be negative. So, the negative sign will get rejected.

⇒ ± 8 Reject -ve = a

⇒ 8 = a

Value of a = 8

Hence, the three sides of the equilateral triangle = 8 cm

Using formula,

• Perimeter = 3a

Substituting the given values :

⇒ Perimeter = 3 × 8

⇒ Perimeter = 24

Therefore, the perimeter of the equilateral triangle = 24 cm