Question

Maria plans to use fencing to build an enclosure or enclosures for her two horses. A single enclosure would be square shaped and require an area of 2,025 ft2. Two individual adjacent enclosures would be rectangular, with dimensions 20 ft by 40 ft with a 40 ft divider between the two enclosures. A square and a rectangle are shown. The square has an area of 2,025 feet squared. The rectangle is comprised of 2 rectangles that are 20 by 40 feet long. Which statement explains the design Maria should choose to minimize her costs? The singular enclosure would minimize cost because it requires 180 feet of fencing. The singular enclosure would minimize cost because it has the smallest area. The two individual enclosures would minimize cost because they require 200 feet of fencing. The two individual enclosures would minimize cost because they have the largest area.

Answer 1

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;

• The singular enclosure would minimize cost because it requires 180 feet of fencing.

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;

The singular enclosure would minimize cost because it requires 180 feet of fencing.

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