Question

the area of an equaliteral Triangle is
16_/3 Find Find the length of each side and perimeter of the triangle.​

Answer 1

♦ The length of each side of the equilateral triangle is 8 cm

♦ The Perimeter of the equilateral triangle is 24 cm

Given :-

• The area of an equilateral triangle is 16√3 cm².

To find :-

• The length of each side of the triangle.

• The Perimeter of the triangle.

Solution :-

Let the each side of an equilateral triangle be a cm

We know that

Area of an equilateral triangle is

(√3/4) a² sq.units

Therefore, (√3/4) a² = 16√3

=> a² = 16√3×(4/√3)

=> a² = (16×√3×4)/√3

=> a² = 16×4

=> a² = 64

=> a = ±√64

=> a = ±8

=> a = 8 cm

Since, The length of the side can't be negative.

Therefore, The length of the each side is 8 cm

We know that

The Perimeter of an equilateral triangle is 3a units

Perimeter of the given equilateral triangle

= 3(8) cm

= 24 cm

Answer :-

♦ The length of each side of the equilateral triangle is 8 cm

♦ The Perimeter of the equilateral triangle is 24 cm

Used formulae:-

♦ Area of an equilateral triangle is (√3/4) a² sq.units

♦ The Perimeter of an equilateral triangle is 3a units

• a = side

Answer 2

GIVEN :-

the area of an equaliteral Triangle is

16√3

TO FIND :-

• Find the length of each side and perimeter of the triangle = ?

SOLUTION :-

Given area of equilateral triangle is 16√3cm², Now we know that area of equilateral triangle

is √3/4 (side)²

√3/4 (side)² = 16√3

side² = 4 × 16

side² = 64

side = 8cm

Now perimeter of an equilateral triangle is given by 3 (side)

Perimeter of an equilateral triangle = 3(8)cm

= 24cm

Perimeter of an equilateral triangle

is 24 cm.