The area of the rectangle can be represented by the expression a = 160l - l² if the field of length l and width w has a perimeter of 320 yards.
What is a rectangle?
It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that:
A field of length l and width w has a perimeter of 320 yards.
As we know, the perimeter of the rectangle = 2(l + w)
2(l + w) = 320
l + w = 320/2
l + w = 160
The area of the rectangle = lxw
Let a is the area of the rectangle.
a = lw
Plug w = 160 - l in the above equation:
a = l(160 - l)
a = 160l - l²
The above expression represents the area of the rectangle in terms of l.
Thus, the area of the rectangle can be represented by the expression a = 160l - l² if the field of length l and width w has a perimeter of 320 yards.
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