CUET · MATHS · PYQ PAPER 2023
The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.
If \(x\) and \(y\) represent the length and breadth of rectangular region the whole area of window is maximum, then value of \(x\) is :
- A \(\frac{20}{\pi}\)
- B \(\frac{20}{4-\pi}\)
- C \(\frac{20}{2+\pi}\)
- D \(\frac{20}{4+\pi}\)
Answer & Solution
Correct Answer
(D) \(\frac{20}{4+\pi}\)
Step-by-step Solution
Detailed explanation
Perimeter \(P = x + 2y + \frac{1}{2} (2\pi \frac{x}{2}) = x + 2y + \frac{\pi x}{2}\) \(10 = x + 2y + \frac{\pi x}{2}\) \(2y = 10 - x - \frac{\pi x}{2} = 10 - x(1 + \frac{\pi}{2})\) \(y = 5 - x(\frac{2+\pi}{4})\) Area…
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