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?
Let's first calculate the original area of the plot.
Original area = length x width
Original area = 200m x 300m
Original area = 60000m^2
After doubling in size, the new area of the plot is twice the original area:
New area = 2 x Original area
New area = 2 x 60000m^2
New area = 120000m^2
Now, let's express the new length and width in terms of x:
New length = 200 + x
New width = 300 + x
So, the new area in terms of x is:
New area = (200 + x)(300 + x)
120000 = 60000 + 200x + 300x + x^2
120000 = x^2 + 500x + 60000
Rearranging the equation into standard form:
x^2 + 500x - 60000 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula.
Factoring:
(x + 600)(x - 100) = 0
x = -600 or x = 100
Since the length and width cannot be negative, the value of x is 100 meters.