Question

a rectangle initially has dimensions 4 cm by 8 cm. all sides begin increasing in length at a rate of 4 cm /s. at what rate is the area of the rectangle increasing after 20 s?

Answer 1

688 cm²/s

Explanation:

You want to know the rate of increase of area of a rectangle that is initially 4 cm by 8 cm, with side lengths increasing at 4 cm/s.

Area

The area is the product of the side lengths. Each of those can be written as a function of time:

L = 8 +4t

W = 4 +4t

A = LW = (8 +4t)(4 +4t)

Rate of change

Then the rate of change of area is ...

A' = (4)(4 +4t) + (8 +4t)(4) = 32t +48

When t=20, the rate of change is ...

A'(20) = 32·20 +48 = 640 +48 = 688 . . . . . . cm²/s

The area is increasing at the rate of 688 square centimeters per second after 20 seconds.