Question

The area of a circle is given by the expression πx² + 6πx + 9π. Find the radius of the circle.

Answer 1

We have,

Area of a circle = πx² + 6πx + 9π = π(x² + 6x + 9)

⇒ πr² = π(x² + 3x + 3x + 9)  ...[∵ Area of a circle = πr², where r is the radius]

⇒ πr² = π[x(x + 3) + 3(x + 3)] = π(x + 3)(x + 3) = π(x + 3)²

⇒ πr² = π(x + 3)²

On comapring both sides, r² = (x + 3)² ⇒ r = x + 3

Hence, the radius of circle is x + 3.