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

Updated On: Oct 3, 2024
  • 24√3 cm2
  • 24√2 cm2
  • 64√3 cm2
  • 32√3 cm2
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The Correct Option is C

Solution and Explanation

Assume the perimeter of square and equilateral triangle be 12x cm12x\ cm

The side of square = 12x4\frac{12x}{4} = 3x3x

Side of Triangle = 4x4x

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

3x×2=1223x × \sqrt{2} = 12\sqrt{2}

x=123=4x = \frac{12}{3} = 4

Sides of Triangle = 4 × 4 = 16 cm

Area of equilateral triangle = 34cm2\frac{\sqrt{3}}{4} cm^2

34×(16)×(16)\frac{\sqrt{3}}{4} × (16) × (16)

643cm264\sqrt{3} cm^2

The correct option is (C): 64√3 cm2

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