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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

Respuesta :

MrRoyal

Answer:

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

Step-by-step explanation:

Given

Single enclosure

[tex]Area = 2025ft^2[/tex] --- of square

Two adjacent enclosures

[tex]Dimension= 20ft\ by\ 40ft[/tex] ---- both rectangles

[tex]Divider = 40ft[/tex]

Required

Determine the true statement to minimize cost

Start by calculating the perimeter of the single enclosure.

Let

[tex]l \to[/tex] length of the enclosure (square shape)

So:

[tex]Area = l^2[/tex]

[tex]2025 = l^2[/tex]

Rewrite as:

[tex]l^2 = 2025[/tex]

Take square roots

[tex]l = 45[/tex]

The perimeter (P) is then calculated as:

[tex]P = 4l[/tex]

[tex]P = 4 * 45[/tex]

[tex]P_1 = 180ft[/tex]

Next, the perimeter of the two enclosures.

Let

[tex]l \to[/tex] length of the enclosure

[tex]w \to[/tex] width of the enclosure

[tex]l = 20[/tex]

[tex]w =40[/tex]

The perimeter of 1 enclosure is:

[tex]P = 2(l + w)[/tex]

[tex]P = 2(20 + 40)[/tex]

[tex]P = 2*60[/tex]

[tex]P = 120[/tex]

For 2 enclosures

[tex]P_2 =2 * P[/tex]

[tex]P_2 =2 * 120[/tex]

[tex]P_2 =240[/tex]

Remove the length of the divider

[tex]P_2 = 240 - 40[/tex]

[tex]P_2 = 200ft[/tex]

By comparison;

[tex]P_1 < P_2[/tex]

i.e.

[tex]180ft < 200ft[/tex]

Hence, the singular enclosure will minimize costs

alexandraresendiz3

Answer:

A

Step-by-step explanation:

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