CUET · MATHS · PYQ PAPER 2025
The length of a rectangle is decreasing at the rate of \(4\) cm / minute and the width is increasing at the rate of \(3\) cm / minute , then the rate of change of the perimeter is
- A \(2\) cm / min decreasing
- B \(3\) cm / min decreasing
- C \(2\) cm / min increasing
- D \(3\) cm / min increasing
Answer & Solution
Correct Answer
(A) \(2\) cm / min decreasing
Step-by-step Solution
Detailed explanation
\(P = 2L + 2W\) \(\frac{dP}{dt} = 2\frac{dL}{dt} + 2\frac{dW}{dt}\) \(\frac{dP}{dt} = 2(-4) + 2(3)\) \(\frac{dP}{dt} = -8 + 6 = -2 \, \text{cm/min}\) The rate of change of the perimeter is \(2 \, \text{cm/min}\) decreasing.
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