Question

Two circles have diameters x and y. Show that a circle with diameter z = √x² + √y² has the same area as the two circles together.

​

Answer 1

Explanation step by step:

Area = πr²

Radius = Diameter / 2

Circle with diameter x

Radius = x / 2

Area Cx = π(x/2)²

Area Cx = πx²/4

Circle with diameter y

Radius = y / 2

Area Cy = π(y/2)²

Area Cy = πy²/4

Area of the two circles, x and y

Area Cxy = Area Cx + Area Cy

Area Cxy = πx²/4 + πy²/4

Area Cxy = (πx² + πy²)/4

Area Cxy = π(x² + y²)/4

Circle with diameter z

Radius = (√x² + √y²) / 2

Area Cz = π((√x² + √y²) / 2)²

(√x²)² = (x^(2/2))² = x^(4/2) = x²

Area Cz = π(x² + y²)/4

Proof

Area Cxy = Area Cz

π(x² + y²)/4 = π(x² + y²)/4

Answer 2

Respuesta:

sorry not speak inglish

Explicación paso a paso:

sorry boy ylgu