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

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

Step-by-step explanation:

Given

Single enclosure

--- of square

Two adjacent enclosures

---- both rectangles

Required

Determine the true statement to minimize cost

Start by calculating the perimeter of the single enclosure.

Let

length of the enclosure (square shape)

So:

Rewrite as:

Take square roots

The perimeter (P) is then calculated as:

Next, the perimeter of the two enclosures.

Let

length of the enclosure

width of the enclosure

The perimeter of 1 enclosure is:

For 2 enclosures

Remove the length of the divider

By comparison;

i.e.

Hence, the singular enclosure will minimize costs

6e14 is the answer.