Question

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?

Answer 1

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