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
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2 cm/min decreasing
Let the length be l and the width w. The perimeter is
\(P = 2(l + w)\)
Differentiating with respect to time t:
\( \displaystyle \frac{dP}{dt} = 2\left(\frac{dl}{dt} + \frac{dw}{dt}\right) \)
A decreasing length has a negative rate: \(\frac{dl}{dt} = -4\) and \(\frac{dw}{dt} = 3\). So
\( \displaystyle \frac{dP}{dt} = 2(-4 + 3) = -2 \)
The minus sign means the perimeter is decreasing at 2 cm/min.
NCERT (2026-27 edition):
Rate of Change of Quantities
