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

Answer: (C)

64√3 cm2

Answer 2

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