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?
x = [ ]
In order to find the value of x, we first need to calculate the area of the original plot.
Area = length x width
Area = 200 meters x 300 meters
Area = 60,000 square meters
Since the area of the new plot is double the original plot, the area is now 120,000 square meters.
Now, we can set up an equation to find the value of x:
(200 + x)(300 + x) = 120,000
Expanding the equation:
60,000 + 200x + 300x + x^2 = 120,000
x^2 + 500x - 60,000 = 0
Now we can use the quadratic formula to solve for x:
x = (-500 ± √(500^2 - 4(-60,000)) / 2
x = (-500 ± √(250,000 + 240,000)) / 2
x = (-500 ± √490,000) / 2
x = (-500 ± 700) / 2
x = (200 or -300)
Since the length and width can't be negative, the value of x is 200.
Thus, x = 200 meters.
are you sure
Let's double check the calculations:
Given:
Original Length = 200 meters
Original Width = 300 meters
Original Area = Length x Width
Original Area = 200 meters x 300 meters
Original Area = 60,000 square meters
Double the Area = 120,000 square meters
Now we can set up an equation to solve for x:
(200 + x)(300 + x) = 120,000
200*300 + 200x + 300x + x^2 = 120,000
60,000 + 500x + x^2 = 120,000
Rearranging the above equation:
x^2 + 500x - 60,000 = 0
Now, we can solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-500 ± √((500)^2 - 4(1)(-60,000))) / 2
x = (-500 ± √(250,000 + 240,000)) / 2
x = (-500 ± √490,000) / 2
x = (-500 ± 700) / 2
x = (200 or -700)
Since the width and length of the plot cannot be negative, the value of x should be positive. Therefore, x = 200 meters.
So, it seems like the value of x is indeed 200 meters. Thank you for pointing that out.