Question

The radius of a circle is greater than the radius of other circle by 3m.The sum of their areas is 89πm².Find the radius of each circle

Answer 1

Answer:

Step-by-step explanation:

Let the radius ,rof other circle by x m

Therefore, radius of first circle, R= x+3.

ATQ,

Area of first circle + Area of other circle = 89πm^2

πR^2+πr^2=89π

π(R^2+r^2)= 89π

(x+3)^2+(x)^2= 89

x^2+9+6x+x^2=89

2x^2+6x+9-89=0

2x^2+6x-80=0

Divide by 2 both sides,

x^2+3x-40=0

By middle term splitting method,

x^2+8x-5x-40=0

x(x+8)-5(x+8)=0

(x+8)(x-5)=0

Therefore, x= 5 cm

We didn't take -8 as the radius of circle will never be in negative numbers.