A rectangular plot of land is 4 meters longer than it is wide. It's surrounded by a multicolored walk 1 m wide. The area of the walk is 32 m. What are the dimensions of the pool?
area of plot = x(x+4)
area of pool = (x-2)(x+2)
so x(x+4) - (x-2)(x+2) = 32
solve for x, sub into x-2 and x+2
(I got x=7)
Where did you get the x-2?
If the plot is 7 m wide and there is a walkway of 1 m on either side of the pool, isn't the pool 5 m wide?
so 7-2
or x-2
that is also how I got x+2 for the length of the pool, it was x+4, now take away 1 m from each side.....
Thanks!
To find the dimensions of the pool, we need to first find the dimensions of the rectangular plot of land.
Let's assume the width of the rectangular plot is "x" meters. Since the length is 4 meters longer, the length would be "x + 4" meters.
Now, to find the area of the rectangular plot, we multiply the length by the width.
Area of the rectangular plot = length * width = (x + 4) * x
Since the multicolored walk surrounds the rectangular plot, both the length and width of the plot will increase by 2 meters (1 meter on each side).
So, the length with the walkway will be (x + 4 + 2) and the width with the walkway will be (x + 2).
The area of the walkway is given as 32 m².
To find the area of the walkway, we subtract the area of the plot from the area of the plot with the walkway:
Area of the walkway = (x + 4 + 2)(x + 2) - (x + 4)(x) = 32
Now, let's solve this equation to find the value of x.
Simplifying:
(x + 6)(x + 2) - (x + 4)(x) = 32
(x^2 + 6x + 2x + 12) - (x^2 + 4x) = 32
x^2 + 8x + 12 - x^2 - 4x = 32
4x + 12 = 32
4x = 32 - 12
4x = 20
x = 20/4
x = 5
Therefore, the width of the rectangular plot is 5 meters.
The length of the rectangular plot is (5 + 4) = 9 meters.
Hence, the dimensions of the pool are 5 meters by 9 meters.