Question

if the area of a square is 100 cm and its perimeter is the same as the perimeter of an equilateral triangle , what is the length of each side of the triangle

Answer 1

Formulas related to this topic are given below : -

$\boxed{\mathsf{Area\:of\:square=side^2}}\\\boxed{\mathsf{Perimeter\:of\:square=4\:\texttt{x} \:side} }\\\boxed{\mathsf{Perimeter\:of\:equilateral\:triangle=3\:\texttt{x}\: side}}$

On the basis of the formulas given above,

Given, Area of square = 100 cm^2

⇒ side^2 = 100 cm^2

⇒ side^2 =  ( 10 cm )^2

⇒ side = 10 cm

Perimeter of the square = 4 x side

⇒ 4 x ( 10 cm )

⇒ 40 cm

Given that the perimeter is the same as the perimeter of an equilateral triangle.

∴ 40 cm = perimeter of the triangle

⇒ 40 cm = 3 x side

⇒ 40 cm / 3 = side

⇒ 40 / 3 cm = side

Hence, length of each side of the equilateral side is 40/3 cm.

Answer 2

Here is your solution

Given :-

area of a square is 100 cm^2

side × side = 100 cm^2

side = 10cm

perimeter of square = 4×side
=>4×10 = 40cm.

Given:- Perimeter of triangle = perimeter of square

A/q

perimeter of equilateral triangle = 3×side

40cm = 3×side

side = 40/3cm

side of equilateral triangle =40/3cm

Hope it helps you