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The perimeter of a square and an equilateral triangle is equal. If the diagonal of the square is 12√2 cm, then area of the triangle. |
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Answer» Let diagonal of the square be 12√2 cm. If each side of the square be a cm then a√2=12√2 =>a=12 cm So the perimeter of the square is =4×12=48cm. Which is also the perimeter of an equilateral triangle. Hence each side of the equilateral triangle is 48/3=16cm. Then the area of the triangle becomes √3/4×16^2cm^2=64√3cm^2 Diagonal of a square =12√2 cm If each side of the square be a cm then a√2 = 12√2 cm a = 12 cm Side if square = 12 cm Perimeter of square = 4 x side = 4 x 12 cm = 48 cm Perimeter of equilateral triangle = 3a where a is side of the triangle 48 cm = 3a a = 48/3 cm = 16 cm Area of equilateral triangle = √3/4 a2 = √3/4 x 16 cm x 16 cm = 64 √3 cm2 |
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