Question

The area of a circle is equal to the sum of the area of a rectangle and a square. The length of the rectangle is 1 cm more than the twice of the side of the square and breadth of the rectangle is 1.5 cm less than \(\frac{3}{2}\) times of the radius of the circle. What is the difference between the circumference of the circle and perimeter of the square if the side of the square is 6 cm less than the radius of the circle?

• A. 110 cm
• B. 104 cm
• C. 103 cm
• D. 105 cm

Answer 1

The Correct Option is B

The correct option is (B): 104 cm.
Let radius of the circle = r cm
The side of the square = (r - 6) cm
Length of the rectangle = 1 + 2(r - 6) = 1 + 2r - 12 = (2r - 11) cm
Breadth of the rectangle = (1.5r - 1.5) = 1.5(r - 1) = 3\(\frac{(r - 1)}{2}\) cm
According to the question,
πr2 = L * B + a2
=> 22/7 * r2 = (2r - 11) * 3\(\frac{(r - 1)}{2}\) + (r - 6)2
=> 44r2 = 21(2r2 - 13r + 11) + 14(r2 - 12r + 36)
=> 44r2 = 42r2 - 273r + 231 + 14r2 - 168r + 504
=> 44r2 = 56r2 - 441r + 735
=> 12r2 - 441r + 735 = 0
=> 4r2 - 147r + 245 = 0
=> 4r2 - 140r - 7r + 245 = 0
=> 4r(r - 35) - 7(r - 35) = 0
=> r = 35 or \(\frac{7}{4}\)
Thus, Let radius of the circle = 35 cm
The side of the square = 29 cm
So, difference = 2πr - 4a = 2 * \(\frac{22}{7}\)* 35 - 4 * 29 = 104 cm