The two enclosures require fencing for partitioning and its combined
external dimension is less than the dimension of the single enclosure.
The statement that provides the reason for the design Maria should
choose to minimize her cost is the option;
- <u>The singular enclosure would minimize cost because it requires 180 feet of fencing</u>.
Reasons:
The area of the singular enclosure, A = 2,025 ft.²
Dimension of each of the adjacent enclosures = 20 ft. by 40 ft.
The length of the divider between the two rectangular adjacent enclosures = 40 ft.
Required:
The statement that represent the solution Maria should choose to minimize cost.
Solution:
The length of fencing for the singular square enclosure is given by the perimeter of the square as follows;
Perimeter of a square = 4·s
Area of a square = s²
Therefore, for the singular square enclosure, we have;
s² = 2,025 ft.²
Which gives;
s = √(2,025 ft.²) = 45 ft.
The perimeter of the singular enclosure = 4·s = 4 × 45 ft. = 180 ft.
The perimeter of the two individual adjacent enclosure is given as follows;
P = 2 × (20 ft. + 20 ft.) + 2 × 40 ft. + 40 ft. = 200 ft.
The area of the two individual adjacent, A = 2 × 20 ft. × 40 ft. = 1,600 ft.²
Therefore, given that the area of the single enclosure, is larger and that the
length of fencing of the singular enclosure is lesser than the two individual
adjacent enclosures, we have;
To minimize cost, Maria should choose the singular enclosure that require
180 feet of fencing compared to two adjacent enclosures that require 200
feet of fencing.
The correct option that gives the reason of the design Maria should choose is therefore;
<u>The singular enclosure would minimize cost because it requires 180 feet of fencing</u>.
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