The sum of the areas of two circles P and Q is 20020 cm2. If the product of the diameters of both circles P and Q is 12348 cm, then find out the sum of the radius of both of the circles.

Let’s assume the radius of circles P and Q are ‘R’ and ‘r’.

The sum of the areas of two circles P and Q is 20020 cm².

πxR² + πxr²  = 20020

π(R²  + r² ) = 20020

22/7(R²  + r² ) = 20020

(R² + r² ) = 20020x(7/22)

(R²  + r² ) = 6370    Eq.(i)

If the product of the diameters of both circles P and Q is 12348 cm.

2Rx2r = 12348

4Rr = 12348

2Rr = 6174    Eq.(ii)

Sum of the radius of both of the circles = (R+r)

Make a square with the help of a formula.

(R+r)²  = R² +r² +2Rr

Put Eq.(i) and Eq.(ii) in the above equation.

(R+r)²  = 6370+6174

(R+r)²  = 6370+6174 = 12544

So the sum of the radius of both of the circles = (R+r) = 112 cm