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?
The area of the original plot is 200 x 300 = 60000
So the problem says
(x + 200)(x + 300) = 120000
Proof: 300 x 400 = 120000
x^2 + 500x + 60000 = 120000
x^2 + 500x - 60000 = 0
(x + 600)(x - 100) = 0, so
x = - 600 (reject), x = 100
So x = 100 meters
Proof: 300 x 400 = 120000