The length of a rectangle is decreasing at 4 cm/minute and the width is increasing at 3 cm/minute. The rate of change of area when length is 10cm and width is 6cm, is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 cm2/minute
Let the length be l and the width w, so the area is \( A=lw \). By the product rule,
\( \displaystyle \frac{dA}{dt}=l\,\frac{dw}{dt}+w\,\frac{dl}{dt} \)
The length is decreasing, so \( \frac{dl}{dt}=-4 \); the width is increasing, so \( \frac{dw}{dt}=3 \). At l = 10 and w = 6:
\( \displaystyle \frac{dA}{dt}=10(3)+6(-4) \)
\( \displaystyle =6 \)
The area is increasing at 6 cm2/minute.
NCERT (2026-27 edition):
Rate of Change of Quantities
