Question

The area of a circle is given by the expression - (πx^2+10πx+25π) find the radius of the circle

Answer 1

Step-by-step explanation:

$\large\underline{\bf \orange{Given :}} \\Area \: of \: circle = πx² + 10πx + 25π \\\large\underline{\bf \orange{To \: Find :}} \\Radius \: of \: the \: circle \\\large\underline{\bf\orange{Solution :}} \\\begin{gathered}\implies\underline{\boxed{ \bf Area \: of \: circle = {\pi r}^{2} }} \\ \\ \implies\sf \pi {x}^{2} + 10\pi x + 25\pi = {\pi r}^{2} \\ \\\implies\sf \cancel \pi ({x}^{2} + 10x + 25)= \cancel\pi( { r}^{2}) \\ \\ \implies\sf {r}^{2} = {x}^{2} + 10x + 25 \\ \\\implies\sf {r}^{2} = {x}^{2} + 5x + 5x + 25 \\ \\\implies\sf {r}^{2} = x( x+ 5) + 5(x + 5) \\ \\\implies\sf {r}^{2} = (x + 5)(x +5) \\ \\\implies\sf {r}^{2} =\sqrt{(x+5)^2 }\\ \\\implies\underline{\boxed{\sf r = x+5}} \end{gathered} \\ ⟹Area \: of \: circle=πr2 \\ ⟹πx2+10πx+25π=πr2 \\ ⟹π(x2+10x+25)=π(r2) \\ ⟹r2=x2+10x+25 \\ ⟹r2=x2+5x+5x+25 \\ ⟹r2=x(x+5)+5(x+5) \\ ⟹r2=(x+5)(x+5) \\ ⟹r2=(x+5)2 \\ ⟹r=x+5$