Question

The area of an equilateral triangle is numerically equal to its perimeter.Find the length of its side correct to two decimal place. Answer :- 6.93 unit.​

Answer 1

Answer:

6.93 unit

Step-by-step explanation:

Let the length of the side of the equilateral triangle 'a'.

   Perimeter of equilateral triangle = 3a

   Area of equilateral triangle = a²(√3)/4

Given:  both are numerically equal

         ⇒ 3a = a²√(3)/4

         ⇒ 12a = a²√3

         ⇒ 0 = a²√3 - 12a

         ⇒ 0 = √3a(a - 4√3)

Using zero-product rule:

  ⇒ 0 = √3a    or   0 = a - 4√3

  ⇒ 0 = a        or 4√3 = a

  ⇒ 0 = a       or 6.93 = a

Excluding a = 0(it says 'triangle  doesn't exist')

       ∴ a = 6.93 unit

Answer 2

for further explanation please refer the given attachment