Question

Area of an equilateral triangle is 4√3 cm². Then the length of diagonal of a square whose side is equal to the height of equilateral triangle is
1. 2√6
2. 3√6
3. 2√3
4. 3√2

Answer 1

Correct Answer - Option 1 : 2√6

Given:

Area(A) of the equilateral triangle = 4√3 cm²

Formula used:

Area of an equilateral triangle = (√3/4)a²; a = length of the side of the triangle

Area of a triangle = bh/2; b = base(side) of the triangle, h =height of the triangle 

Area of a square = x²

Diagonal of a square = √2x 

x = length of the side of the square

Calculation:

According to the question:

(√3/4)a² = 4√3

⇒ a = 4 cm = b

Also, 4√3 = bh/2

⇒ 4√3 = 4h/2

⇒ h = 2√3 = x

Diagonal of the square = √2x = √2(2√3)

∴ Diagonal of the square = 2√6 cm