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A square and an equilateral triangle have the same perimeter. If the area of the triangle is 16√3 , what is the area of the square?

Let the side of Equilateral triangle be t And of square be s By first condition 4*s = 3*t Area of equilateral triangle = √3/4 * (side^2) = √3/4 * (t^2) 16√3/4 = √3/4 * (t^2) So t^2 = 16*4 t = 8 Now 4*s = 3*8 s = 6 So area of square = side^2 = 6^2 = 36

Let x as side of triangle, y as side of square. hence 3x = 4y area of triangle = 1/2 bh, b = x , h = √3 x /2 hence √3x^2 / 4 = 16√3 x = 8 3x = 24 = 4y y = 6 area of square = y^2 = 36.............

let side of the triangle be b then area of the triangle is 0.5*b*0.5*b*sqrt(3) given area of the triangle is 16*sqrt(3) from the above two b=8 therefore side of the square is 6 and area 36

Suppose you have perimeter as 12x then each side of triangle would be 3x and for square it would be 4x.

now (√3/4)*(4x)^2 = 16√3 or (4x)^2 = 64 = 8^2 or x = 2

area of the square is (3x)^2 or 36

Let the side of the equilateral be s, then area of the equilateral ▲= (√3s²)/4 = 16√3 => s² = 64 → s = 8

Perimeter of the equilateral ▲= 3s = 24

Perimeter of the square = 4a = 24, hence a= 6.

Area of the square a² = 6² = 36

The area of square would be 32.

A triangle, a square, a pentagon, a hexagon, an octagon and a circle all have an equal perimeter, which one has the smallest area?

ABCD is a square and point P inside the square is such that PCD is an equilateral triangle. Find the angle α

In a circle of radius 1, an equilateral triangle is inscribed in the circle as shown. What is the area of the blue region?