Question

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

Answer 1

Given that area of the circle is

$A=\pi x^2+10 \pi x + 25 \pi$...(i)

Question is talking about area of circle so that gives us hint that we need to use formula of the area of circle. which is

$A=\pi r^2$...(ii)

where r is called radius.

Equation (i) and (ii) both represents same area of circle so their values must be equal.

we get equation:

$\pi r^2=\pi x^2+10 \pi x + 25 \pi$

factor out pi from the right side

$\pi r^2=\pi (x^2+10x + 25)$

divide both side by pi

$r^2=x^2+10x + 25$

factor the right side more

$r^2=x^2+5x+5x + 25$

$r^2=x(x+5)+5(x + 5)$

$r^2=(x+5)(x + 5)$

$r^2=(x+5)^2$

take square root of both sides

$r=x+5$

Hence radius of the circle is $r=x+5$.

Answer 2

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