A Wire in the form of a circle, encloses an area 3118.5 cm². It is now bent to form a rectangle whose length and breadth are very nearly in the ratio 7 : 4. The length of the rectangle, in cm, is:(Take $π =\frac{22}{7}$)

63

We know that,

Area of circle = πr²

Perimeter of rectangle = 2(l + b)

πr² = 3118.5

= \(\frac{22}{7}\) × r² = 3118.5

= r² = 3118.5 × \(\frac{7}{22}\)

= r² = 141.75 × 7

= r² = 20.25 × 7 × 7

= r = 4.5 × 7 = 31.5

Circumference of circle = 2πr = 2 × \(\frac{22}{7}\) × 31.5 = 198

Here,

Circumference of the circle = Perimeter of rectangle

Ratio of length and breadth of the rectangle = 7x : 4x

2(7x + 4x) = 198

= 2 × 11x = 198

= x = \(\frac{198}{22}\) = 9

Length of the rectangle = 7x = 7 × 9 = 63