A rectangular field is to be fenced off with 120 m of fencing materials. the length of the field is x. express the area in square meters of the field as a function of x.
f(x)=(120m^3)x
nice try, but you're mixing things up. Why do you say 120 m^3? m^3 is volume, not are or length! And why multiply the perimeter by the length, anyway?
Just take a step back and work things out.
The area is length * width
The 120m of fencing reaches around the field -- that is the perimeter.
If the perimeter is 120, that means that
2(length+width)=120
length+width=60
So, if the length is x,
width = 60-x
That means that the area is
x(60-x)
and that is in m^2: meters * meters
To express the area of the rectangular field as a function of the length (x), we need to use the given information that the field is fenced off with 120 m of fencing materials.
Let's consider the dimensions of the rectangular field. It has a length (L) and a width (W).
Since the field is rectangular, we know that the total length of fencing required is equal to the sum of the length and width of the field, multiplied by 2 (accounting for both sides):
2L + 2W = 120
We can simplify this equation further:
2L + 2W = 120
L + W = 60
Now, since the length of the field is x (as given in the question), we can substitute x for L in the equation:
x + W = 60
W = 60 - x
We have now expressed the width (W) as a function of x.
Next, we need to find the area of the rectangular field. The formula to find the area of a rectangle is:
Area = Length * Width
Substituting the values we have:
Area = x * (60 - x)
Area = 60x - x^2
Therefore, the area of the rectangular field (A) in square meters is expressed as a function of x:
A(x) = 60x - x^2