Question

The radius of a circle is less than twice the radius of the other by 1 cm.
The sum of their areas is 34π sq.cm. Find the radius of each circle.​

Answer 1

Radius of 1st circle is 5cm and second circle is 3cm.

You can refer to the attached image.

Step-by-step explanation:

Let the radius of second circle be r and first circle be 2r-1.

Ar. of 1st circle+ Ar. of 2nd circle= 34π

πr^2 + π (2r-1)^ 2 = 34π

π{ r^2 + (2r-1)^2} = 34π

π(r^2 +4r^2+1-4r) = 34π

5r^2 -4r+1-34 =0

5r^2 -4r -33 =0

5r^2-15r +11r -33=0

5r(r-3) +11(r-3) =0

(r-3) (5r+1)=0

r=3 or r= -1/5 ( Radius cannot be negative)

Therefore, radius of 1st circle = 2*3-1=5cm

Radius of second circle =3cm.

HOPE IT HELPS YOU BUDDY!!

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