Question

The length of a rectangle is increasing at a rate of 8 cmys and its width is increasing at a rate of 3 cmys. When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

Answer 1

Answer:

The area of the rectangle increasing at the rate of 140 cm²/s

Step-by-step explanation:

Rectangle area:

A rectangle has two dimensions, length l and width w.

It's area is:

A = l*w.

When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

We apply implicit differentiation to solve this question:

$A = l*w$

So

$\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

Length is 20, so $l = 20$.

Width is 10, so $w = 10$

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s.

This means that $\frac{dl}{dt} = 8, \frac{dw}{dt} = 3$

So

$\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

$\frac{dA}{dt} = 20*3 + 10*8 = 140$

Area in cm².

So

The area of the rectangle increasing at the rate of 140 cm²/s