An equilateral triangle and a regular hexagon have equal perimeters. T

1.	An equilateral triangle and a regular hexagon have equal perimeters. The ratio of the area of the triangle and that of the hexagon will be1). 1 : 12). 2 : 33). 3 : 24). 3 : 4
Answer» Let the side of the EQUILATERAL triangle be ‘X’. Perimeter of the triangle = 3x Let the side of the REGULAR hexagon be ‘y’ ⇒ Perimeter of regular hexagon = 6y ∴ 6y = 3x 2y = x y = x/2 ----- (1) Area of an equilateral triangle = √3x²/4 Area of regular hexagon = 3√3y²/2 = 3√3x²/8 From (1) ∴ Ratio = (√3x²/4)/(3√3x²/8) = 2 : 3

An equilateral triangle and a regular hexagon have equal perimeters. The ratio of the area of the triangle and that of the hexagon will be1). 1 : 12). 2 : 33). 3 : 24). 3 : 4

Answer»

Let the side of the EQUILATERAL triangle be ‘X’.

Perimeter of the triangle = 3x

Let the side of the REGULAR hexagon be ‘y’

⇒ Perimeter of regular hexagon = 6y

∴ 6y = 3x

2y = x

y = x/2 ----- (1)

Area of an equilateral triangle = √3x²/4

Area of regular hexagon = 3√3y²/2 = 3√3x²/8

From (1)

∴ Ratio = (√3x²/4)/(3√3x²/8) = 2 : 3

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An equilateral triangle and a regular hexagon have equal perimeters. The ratio of the area of the triangle and that of the hexagon will be1). 1 : 12). 2 : 33). 3 : 24). 3 : 4

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