Question

A satellite camera takes a​ rectangle-shaped picture. The smallest region that can be photographed is a 22​-km by 66​-km rectangle. As the camera zooms​ out, the length l and width w of the rectangle increase at a rate of 33 ​km/sec. How long does it take for the area A to be at least 5 times its original​ size?

Answer 1

find what that area is
22*66=1452

5 times of that is
1452*5=7260


s=seconds

(22+33s)(66+33s)=7260
1089s^2+2904s+1452=7260
minus 7260 from both sides
1089s^2+2904s-5808=0
factor or use quadratic formula
(363)(x+4)(3x-4)=0
set each to zero
x+4=0
x=-4, false, it is increasing, not decreasing

3x-4=0
3x=4
x=4/3

answer is 4/3 seconds