Question

A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?

Answer 1

So we know that the formula for the area of a rectangle is
`A = lw`.
Now both the length and width of the rectangle increase at 3 km/s, therefore,
`A(t) = (3t+l)*(3t+w). Since the initial length = initial width = 4 km, then the initial area = 16 [tex]km^2`. We want to know the time when the area is four times its original area, therefore, our new formula is:
`4A(t) = (3t+l)*(3t+w)`. Plugging in our known values we have:


`64 [km^2] = (3t + 4 [km])*(3t + 4 [km])`

`t = (4)/(3) s`

The area is four times its original area after \frac{4}{3} s[/tex].