Question

The area of a circle is 4πx^2 + 12πx + 9π

A) what is an expression for the radius of the circle?
B) what is the least possible integer value of x for the circle to exist?explain

Please help and explain

Answer 1

r = 2x + 3

Explanation:

`\text{The formula of an area of a circle:}\\\\A=\pi r^2\\\\r-\text{radius}\\\\\text{We have}\ A=4\pi x^2+12\pi x+9\pi=(4x^2+12x+9)\pi=(2^2x^2+2(2x)(3)+3^2)\pi\\\\=\bigg((2x)^2+2(2x)(3)+3^2\bigg)\pi\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=(2x+3)^2\pi\to r=2x+3`