A wire in closes in area of 18634 cm2 when it is bent in the form of circle. The same wire is now bent to form a rectangle whose sides are in the ratio 5:6. the length (in cm) off the shoulder side of the rectangle is (Take π =22/7):
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 110.
Area of the formed circle = 18634 cm2
The ratio of sides of the rectangle = 5 : 6
Area of a circle = πr2
The perimeter of a circle = 2πr
Perimeter of a rectangle = 2(l + b) Here,r = radius of the circle, l = length of the rectangle, b = breadth of the rectangle
Let the radius of the formed circle be r.
πr2 = 18634
r2 = 18634 × 7/22
r2 = 5929
r2 = 772
r = 77
The perimeter of the formed circle will be equal to the perimeter of the rectangle.
Let the sides of the rectangle be 5x and 6x.
So,2 × 22/7 × 77 = 2(5x + 6x)
2 × 22 × 11 = 2 × 11x
11x = 22 × 11
x = (22 × 11)/11
x = 22
Now, Sides of the rectangle = 5 × 22 = 110 cm and 6 × 22 = 132 cm
Thus, the smallest side of the rectangle = 110 cm