The smallest region that can be photographed is 5*7 = 35 square km so we want to know how long it takes to zoom out to an area of 35 * 5 = 175 square km.
Notice that the length and width increase at the same rate, 2 km/sec, and they start out with a difference of two, so when the width has increased from 5 to x, the length will have increased from 7 to x+2. At the desired coverage area, then, x(x+2) = 175 x^2 + 2x = 175 x^2 + 2x + 1 = 176 [completing the square] (x+1)^2 = 176 x+1 = ±4√11 x = -1 ±4√11
Since a negative value for x is meaningless here, x must be -1 + 4√11 = about 12.27 km and the time it took to increast to that value was (12.27 - 5) km / (2 km/sec) = about 3.63 seconds
