Question

The area of an equilateral triangle is numerically equal to its perimeter. Find its perimeter correct to 2 decimal places.

Answer 1

Let the side of an equilateral triangle is a

perimeter of equilateral triangle= area of equilateral triangle

3a= (√3/4)a^2
a= (4×3)/√3
a= (4×3)×√3/ √3×√3. ( by rationalising)
a= 4√3
side = 4√3
perimeter of equilateral triangle= 3a
perimeter of equilateral triangle= 3× 4√3
perimeter of equilateral triangle= 12√3
perimeter of equilateral triangle= 12× 1.732
perimeter of equilateral triangle= 20.78 units

[ value of √3 = 1.732]

Answer 2

Answer: Let the side of an equilateral triangle is a

perimeter of equilateral triangle= area of equilateral triangle

3a= (√3/4)a^2

a= (4×3)/√3

a= (4×3)×√3/ √3×√3. ( by rationalising)

a= 4√3

side = 4√3

perimeter of equilateral triangle= 3a

perimeter of equilateral triangle= 3× 4√3

perimeter of equilateral triangle= 12√3

perimeter of equilateral triangle= 12× 1.732

perimeter of equilateral triangle= 20.78 units

[ value of √3 = 1.73