Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The l
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So we know that the formula for the area of a rectangle is 
.
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](https://tex.z-dn.net/?f=A%28t%29%20%3D%20%283t%2Bl%29%2A%283t%2Bw%29.%20Since%20the%20initial%20length%20%3D%20initial%20width%20%3D%204%20km%2C%20then%20the%20initial%20area%20%3D%2016%20%5Btex%5Dkm%5E2)
. We want to know the time when the area is four times its original area, therefore, our new formula is: 
. Plugging in our known values we have:
![64 [km^2] = (3t + 4 [km])*(3t + 4 [km])](https://tex.z-dn.net/?f=64%20%5Bkm%5E2%5D%20%3D%20%283t%20%2B%204%20%5Bkm%5D%29%2A%283t%20%2B%204%20%5Bkm%5D%29)
The area is four times its original area after <span>\frac{4}{3} s[/tex]</span>.
Now both the length and width of the rectangle increase at 3 km/s, therefore,
The area is four times its original area after <span>\frac{4}{3} s[/tex]</span>.