There are two circular gardens A and B. The circumference of garden A is 1.760 km and the area of garden B is 25 times the area of garden A. Find the circumference of garden B.

Let r be the radius of the circular garden A.

Circumference of garden A = 2πr

⇒ 2πr = 1.760 km

⇒ 2πr = 1760 m

⇒ 2 x $\dfrac{22}{7}$ x r = 1760 m

⇒ $\dfrac{44}{7}$ x r = 1760 m

⇒ r = $\dfrac{7 \times 1760}{44}$ m

⇒ r = 7 x 40 m

⇒ r = 280 m

Area of garden A = πr²

= π x (280)²

= 78400π

Let R be the radius of garden B.

It is given that the area of garden B is 25 times the area of garden A.

⇒ πR² = 25 x πr²

⇒ πR² = 25 x 78400π

⇒ $\cancel{π}$ R² = 25 x 78400 $\cancel{π}$

⇒ R² = 25 x 78400

⇒ R² = 1960000

⇒ R = $\sqrt{1960000}$

⇒ R = 1400 m

Circumference of garden B = 2πR

= 2 x $\dfrac{22}{7}$ x 1400 m

= 2 x 22 x 200 m

= 8800 m = 8.8 km

Hence, the circumference of garden B is 8.8 km.