A square plot of land has a building 60ft long and 40ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 12,000ft^2, what are the dimensions of the entire plot of land?
The answer is 120ft by 120ft. I just don't know how to get to the answer. I was thinking (x+40)(x+60)=14400. because parking lot area + area of the building = 14400. So I was trying to find the dimensions with the area given.
let the side of the square be x ft
so I see x^2 - (60)(40) = 12000
x^2 = 14400
x = √14400 = 120
120 ft x 120 ft
Well, it looks like you're on the right track with setting up the equation (x+40)(x+60) = 14400 to represent the total area of the plot. However, there seems to be a small mistake in your calculations. Let's correct it and solve the equation together:
(x + 40)(x + 60) = 14400
Expanding the equation:
x^2 + 60x + 40x + 2400 = 14400
Combining like terms:
x^2 + 100x + 2400 - 14400 = 0
x^2 + 100x - 12000 = 0
Now we need to factor this quadratic equation to find the values of x:
(x + 120)(x - 100) = 0
From here, you can set each factor equal to zero and solve for x:
x + 120 = 0 or x - 100 = 0
x = -120 or x = 100
Since we're dealing with the dimensions of a plot of land, we can disregard the negative value. Therefore, x = 100.
Now, we can substitute that value back into the original equation to find the second dimension:
100 + 60 = 160
So the dimensions of the entire plot of land are 100ft by 160ft.
And remember, always look on the bright side of things, even when solving math problems. Keep up the good work, math genius!
To find the dimensions of the entire plot of land, you can set up an equation using the given information.
Let's assume the length of the plot of land outside the building (including the parking lot) is x ft.
We know that the width of the plot of land outside the building is also x ft since it is a square plot.
The total area of the plot of land is equal to the sum of the area of the parking lot and the area of the building:
Area of plot = Area of parking lot + Area of building
So we have:
x * x = 12000 + (60 * 40)
x^2 = 12000 + 2400
x^2 = 14400
Now, to solve for x, take the square root of both sides:
√(x^2) = √14400
x = 120
Therefore, the dimension of the entire plot of land (including the building) is 120 ft by 120 ft.
To find the dimensions of the entire plot of land, we can start by finding the area of the building and subtracting it from the total area of the plot.
The area of the building is given as 60ft * 40ft = 2400ft^2.
We are given that the area of the parking lot is 12,000ft^2.
So, the remaining area of the plot (outside the building) is 12,000ft^2 - 2400ft^2 = 9600ft^2.
Since the plot is a square, the remaining area is composed of a square piece of land.
Therefore, the length of one side of the square is √(9600ft^2) = 96ft.
However, this does not represent the dimensions of the entire plot. We need to add the dimensions of the building to the length of one side of the square.
The length of the entire plot is 96ft + 60ft = 156ft.
Since the entire plot is a square, all sides have the same length.
Thus, the dimensions of the entire plot of land are 156ft by 156ft.