A plot of land doubles in size by adding x meters to the length and x meters to the width of the land. If the original plot had an area of 200 by 300 meters, what is the value of x?
original area = a
a = 200 * 300
2a = (200 + x) * (300 + x)
Substitute in the value we know for a.
2(200 * 300) = (200 + x) * (300 + x)
Solve for x.
120,000 = 60,000 + 500x + x2
60,000 = 500x + x2
0 = x2 + 500x - 60,000
0 = (x - 100)(x + 600)
x = 100 or x = -600
Since the question says we are adding length, x must = 100