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

2 cm/min decreasing

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