To find an expression that represents the amount of fencing needed to enclose the rectangular enclosure with two partitions (dividing it into three sections), you can start by determining the perimeter of the enclosure.
Let:
Length of the enclosure be L (in yards).
Width of the enclosure be x (in yards).
The area of the enclosure is given as 540 square yards, so we have:
L * x = 540
To find the perimeter, we need to consider the three segments of fencing: one along the length (2L), and two along the width (2x each). So, the total length of fencing required (P) is:
P = 2L + 2x + 2x = 2L + 4x
Now, we can express the perimeter in terms of x:
P(x) = 2L + 4x
To express the perimeter in terms of x and the given area (540 square yards), we need to solve for L in terms of x using the area equation:
L * x = 540
L = 540 / x
Now, substitute this expression for L back into the perimeter equation:
P(x) = 2(540 / x) + 4x
Simplify:
P(x) = 1080 / x + 4x
So, the expression that represents the amount of fencing needed in terms of x, the width of the enclosure, is:
P(x) = 1080 / x + 4x