Question

The length
x
of a rectangle is decreasing at the rate of 3 cm/minute and
the width
y
is increasing at the rate of 2cm/minute. When
x
=10cm and
y
= 6cm, find
the rates of change of (a) the perimeter and (b) the area of the rectangle.

Answer 1

@terenzreignz

Answer 2

hmm... tricky...
\[\huge P = 2l + 2w\]\[\huge A = lw\]

Answer 3

\[\Large \frac{dl}{dt}=-3\]\[\Large \frac{dw}{dt}=2\]

Answer 4

Thank you Sir

Answer 5

But my instincts say...
\[\huge \frac{dP}{dt}=\frac{\partial P}{\partial l}\cdot{\frac{dl}{dt}}+\frac{\partial P}{\partial w}\cdot\frac{dw}{dt}\]


For area, just replace P with A, accordingly.

Answer 6

oh sorry, I guess replace l with x
and w with y.