The area of a circle is given by the expression πx² + 6πx + 9π. Find the radius of the circle.
Solution:
Given, Area of a circle = πx² + 6πx + 9π
Area of a circle = πr²
⇒ πx² + 6πx + 9π = πr²
⇒ π (x² + 6x + 9) = πr²
⇒ x² + 6x + 9 = r²
⇒ x² + 3x + 3x + 9 = r²
⇒ x(x + 3) + 3(x + 3) = r²
⇒ (x + 3)² = r²
⇒ r = (x + 3)
∴ Radius of the circle = (x + 3)
✦ Try This: The area of the square is given by 16x² + 24x + 9. Find the side of the square.
Area of a square = (side) × (side) = (side)²
Given area of the square is 16x² + 24x + 9
∴ Area of the square, 16x² + 24x + 9 = (side)²
Side = √(16x² + 24x + 9)
= √[(4x)² + 2(4x)(3) + (3)²]
= √(4x + 3)²
= (4x + 3)
∴ Side of the square is (4x + 3).
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9
NCERT Exemplar Class 8 Maths Chapter 7 Problem 101
The area of a circle is given by the expression πx² + 6πx + 9π. Find the radius of the circle.
Summary:
The area of a circle is given by the expression πx² + 6πx + 9π. The radius of the circle is (x + 3)
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