Answer:
180x - x²
Step-by-step explanation:
Since the yard has 360 yd. of fencing, hence the perimeter of Rick's lumberyard has 360 yd.
Given that the yard is x yards long. Let y represent the width of the yard. Hence:
Perimeter of the yard = 2(length + width) = 2(x + y)
Substituting:
360 = 2(x + y)
180 = x + y
y = 180 - x
Therefore the width of the yard is (180 - x) yard.
The area of the yard is the product of the length and the width, hence:
Area (A) = length * width
A = x * (180 - x)
A = 180x - x²
Expression for the area as a function of its length will be, Area = (180x - x²) square yards
It's given in the question,
Since, length of the fence = Perimeter of the rectangular area
And Perimeter of the rectangular area = 2(length + width)
By substituting the values of area and the length in the expression,
360 = 2(x + width)
180 = x + width
Width = (180 - x) yards
Since, area of a rectangle is given by the expression,
Area = Length × Width
By substituting the values in the expression,
Area = x(180 - x)
= (180x - x²) square yards
Therefore, expression for the area in terms of its length will be, Area = (180x - x²) square yards.
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