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 **
Perimeter of a rectangle:
$P = 2(l + w)$
Differentiate w.r.t. time $t$:
$\frac{dP}{dt} = 2\left(\frac{dl}{dt} + \frac{dw}{dt}\right)$
Given:
$\frac{dl}{dt} = -4$ cm/min (length decreasing)
$\frac{dw}{dt} = +3$ cm/min (width increasing)
So,
$\frac{dP}{dt} = 2(-4 + 3)$
$= 2(-1)$
$= -2$
Rate of change of perimeter = -2 cm/min