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The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.
<h3>What is the area of a rectangle?</h3>The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:
Area of a rectangle = length(x) × breath(y)
1000000 sq.ft = (x) × (y) ---- (1)
However, to determine the fencing, we have:
Length of fencing = 2x + 2y
- since the rectangle has four sides and opposite sides are equal
Suppose we use the x-direction to estimate the region where the fencing is located, we have:
Length of fencing = 2x + 2y + x
Length of fencing = 3x + 2y ---- (2)
From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)
The Length of fencing is:
Now, if we replace the value with equation (1), then y will be:
Now, the shortest length of the fencing can be computed by using the equation (2):
L = 3x + 2y
Learn more about the area of a rectangle here: