Question

The area of a circle is given by the (πx² + 10πx + 25π) find the radius of the circle.

( Ma Suman ka bhai hun )​

Answer 1

GIVEN :-

• The area of circle = (πx² + 10πx + 25π).

TO FIND :-

• The radius of the circle.

SOLUTION :-

★ As we know that Area of circle = πr².

→ πr² = πx² + 10πx + 25π

★ Taking π as common.

→ πr² = π(x² + 10x + 25)

→ r² = [π(x² + 10x + 25)]/π

→ r² = x² + 10x + 25

★ Now factorise by " splitting the middle term"

→ r² = x² + 5x + 5x + 25

→ r² = x(x + 5) + 5(x + 5)

→ r² = (x + 5)(x + 5)

→ r = √[(x + 5)(x + 5)]

→ r = √(x + 5)²

→ r = x + 5

Hence the required value for radius of circle is (x + 5) units.

Answer 2

$\large\underline{\bf \orange{Given :}}$

• Area of circle = πx² + 10πx + 25π

$\large\underline{\bf \orange{To \: Find :}}$

• Radius of the circle

$\large\underline{\bf\orange{Solution :}}$

$\implies\underline{\boxed{ \bf Area \: of \: circle = {\pi r}^{2} }} \\ \\ \implies\sf \pi {x}^{2} + 10\pi x + 25\pi = {\pi r}^{2} \\ \\\implies\sf \cancel \pi ({x}^{2} + 10x + 25)= \cancel\pi( { r}^{2}) \\ \\ \implies\sf {r}^{2} = {x}^{2} + 10x + 25 \\ \\\implies\sf {r}^{2} = {x}^{2} + 5x + 5x + 25 \\ \\\implies\sf {r}^{2} = x( x+ 5) + 5(x + 5) \\ \\\implies\sf {r}^{2} = (x + 5)(x +5) \\ \\\implies\sf {r}^{2} =\sqrt{(x+5)^2 }\\ \\\implies\underline{\boxed{\sf r = x+5}}$