Area of the smallest region that can be photographed
![\begin{gathered} =5*7 \\ =35\operatorname{km}^2 \end{gathered}]()
Area which is 5 times its original size
![\begin{gathered} =5*35 \\ =175\operatorname{km}^2 \end{gathered}]()
If the length and width increases at a rate of 2km/sec, its area at any time t (where t is in seconds) will be:

Now, the time it takes for the area A to be at least 5 times its original size will be the time t when:

Next, we solve the equation derived above for t

We can then solve for t using the quadratic formula


Since time cannot be a negative value, the value t=-9.64 seconds is invalid.
Therefore: t=3.64 seconds
Therefore, it would take at least 3.64 seconds for the area, A to be at least 5 times its original size.