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?
is it 100 meters?
No, the value of x is not 100 meters.
To find the value of x, we first need to calculate the area of the original plot. The original plot has dimensions of 200 by 300 meters, so the area is 200 * 300 = 60,000 square meters.
After doubling in size, the new plot has dimensions of (200 + x) by (300 + x) meters. The area of the new plot is then (200 + x) * (300 + x). Since the new plot is twice the size of the original plot, we can set up the equation:
2 * 60,000 = (200 + x) * (300 + x)
120,000 = 60,000 + 500x + x^2
0 = x^2 + 500x - 60,000
0 = (x + 600)(x - 100)
Therefore, x can be either -600 or 100. However, since x represents the added length and width of the plot, it cannot be a negative value. The correct value of x is 100 meters.