Let a large circle with the radius of "a" and the radius of the smaller circle be "b",

As given in the question,

⇒ Difference of areas = 100 cm^2

⇒ Area of large circle - Area of small circle = 100 cm^2

From the properties of circle, we know : -

Area of circle = πr^2, where r is the radius of the circle

= > πa^2 - πb^2 = 100 cm^2

= > π( a^2 - b^2 ) = 100 cm^2

Also, ⇒ Difference of their perimeter = 10 cm

⇒ Perimeter of large circle - perimeter of small circle = 10 cm

From the properties of circle, we know : -

Perimeter of circle = 2πr= > 2πa - 2πb = 10 cm = > 2π( a - b ) = 10 cm

Now,= > π( a^2 - b^2 ) = 100 cm^2 --- ( 1 )

= > 2π( a - b ) = 10 cm --- ( 2 )

Divide ( 1 ) by ( 2 ), we get a + b = 20 cm

Now,= > 2π( a - b ) = 10 cm = > a - b = 10 cm x 1 / 2 x 7 / 22 = > a - b = 35 / 22 cm

Then, adding a + b and a - b,a + b = 20 cma - b = 35 / 22 cm

2a = 20 + 35 / 22 cm

= > 2a = ( 440 + 35 ) / 22 cm= > 2a = 475 / 22 cm= > a = 475 / 44 cm

And, a + b = 20 cm b = 20 cm - 475 / 44 cm b = 405 / 44 cm

Hence, radius of larger circle is 475 / 44 cm and radius of smaller circle is 405 / 44 cm.