Question

A square and an equilateral triangle have the same perimeter. If the diagonal of the square is cm, then the area of the triangle is 12√2 cm, then the area of the triangle is

• A. 24√3 cm²
• B. 24√2 cm²
• C. 64√3 cm²
• D. 32√3 cm²

Answer 1

The Correct Option is C

Assume the perimeter of square and equilateral triangle be \(12x\ cm\)

The side of square = \(\frac{12x}{4}\) = \(3x\)

Side of Triangle = \(4x\)

Diagonal of a square = \(d = \sqrt{2} × side\)

= \(3x × \sqrt{2} = 12\sqrt{2}\)

\(x = \frac{12}{3} = 4\)

Sides of Triangle = 4 × 4 = 16 cm

Area of equilateral triangle = \(\frac{\sqrt{3}}{4} cm^2\)

= \(\frac{\sqrt{3}}{4} × (16) × (16)\)

= \(64\sqrt{3} cm^2\)

The correct option is (C): 64√3 cm2