Question

The radii of two circles are 9cm and 12 cm.fimd the radius of a circle whose area is equal to the sum of the areas of the two circles

Answer 1

area (r=9)=π*81
ar(r=12)=144π
sum area=π(144+81)=225π
πr*r=π(225)
r^2=225
r=15

Answer 2

The radius of the required circle is 15 cm.

Let

      $r_{1} = 9 cm$    

      $r_{2} = 12 cm$

The radius of the circle whose area is equal to the sum of areas of two circles is given by

       $r = \sqrt{r_{1}^{2} + {r_{2}^{2}  }$

                 = $\sqrt{9^{2}+12^{2}  }$

                 = $\sqrt{81 + 144}$

                 = $\sqrt{225}$

                 = 15 cm