Question

The perimeter of a square and equilateral triangle is equal. If the length of

diagonal of the square is 12√2 cm, then what is the area of the equilateral

triangle?

a) 24√2 cm2

b) 4√3 cm2

c)48√3 cm2

d) 64√3 cm2​

Answer 1

Answer = 64√3 cm²

Solution:

Perimeter of square = Perimeter of Equilateral Triangle.

We know that,

In a Square;

Diagonal = √2 × Side

→ 12√2 = √2 × Side

→ Side = 12√2 ÷ √2

→ Side of square = 12 cm

Perimeter of Square = 4 × Side

→ Perimeter of Square = 4 × 12

→ Perimeter of Square = 48 cm

Perimeter of square = Perimeter of Equilateral Triangle

→ 48 = 3 × Side of Equilateral Triangle

→ Side of Equilateral Triangle = 48 ÷ 3

→ Side of Equilateral Triangle = 16 cm

$\sf{Area \:of\:Equilateral\:Triangle=\dfrac{\sqrt{3} }{4}\times (side)^{2} }\\\\\\\implies \sf{Area \:of\:Equilateral\:Triangle=\dfrac{\sqrt{3} }{4}\times 16 \times 16}\\\\\\\implies \boxed{\large{\bf{Area \:of\:Equilateral\:Triangle=64\sqrt{3} \:cm^{2}}}}$