Question

A square has side length x and a circle has radius (x - 1). At what value of x will the two figures have the same area?

Answer 1

x=(π+√π)/1-π

or x=(π-√π)/1-π

Explanation:

since it is a square all sides are equal

Area of square=x*x=x^2

Area of a circle=πr^2

A=π(x-1)^2

two areas are equal

x^2=π(x^2-2x_1)

x^2=πx^2-2πx-π

x^2-πx^2-2πx-π=0

x^2(1-π)-2πx-π=0

using quadratic formula with a=1-π , b=-2π and c=-π

equation of the form ax^2+bx+c=0 by using the quadratic formula:

x=(−b±√b2−4ac)/2a

x=(π+√π)/1-π

or x=(π-√π)/1-π