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 $π =\frac{22}{7}$)
Answer & explanation
Correct answer: option 4
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