Question

The length of a rectangle is increasing at a rate of and its width is increasing at a rate of . when the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

Answer 1

220 cm2/s 
 EXPLINATION

L length of rectangel (cm)

W width of rectangel(cm)

A area of rectangel (cm²)

T time (s)

we are told that:

d1\dt=8cm\s(const),and dw\dt =3cm\s(const)

the area of the rectangel is

A=LW

Differentiating wrt t (using the product rule) we get;

dAdt=(l)(dwdt)+(dldt)(w)

∴dAdt=3l+8w

So when l=20 and w=10⇒
     dAdt=3⋅20+8⋅20
∴dAdt=60+160
∴dAdt=220 cm2/s