Originally Posted by
aidan InitialArea = 5 x 7 = 35
Each side increases at the rate of 2cm/sec
Thus,
The Area at time zero = (5+2*0)(7+2*0) = 35
the area at time of 1 second: (5+2*1)(7+2*1) = 7*9 = 63
the area at time of 2 seconds: (5+2*2)(7+2*2) = 9*11 = 99
the area at time s will be: (5+2*s)(7+2*s)
What we seek is a rectangle that is 5 times the initial area.
5*35 = 175
the area at time in seconds, s : (5+2*s)(7+2*s) = 175
expanding:
5*7 + 10*s + 14*s + 4*s^2 = 175
simplifying:
4s^2 + 24s - 140 = 0
A simple quadratic equation, solve for s.
The actual answer is between the 3rd second and the 4th second.