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

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.