A rancher has 14,000 feet of fence and wishes to enclose a rectangular piece of land on his property with a ratio of the length to width of 4:3.

a. What is the width of the fenced-in lot?

b. What is the area enclosed within the fence in square feet?

c. If one square acre is 43,560 square feet, to the nearest thousandth, how many square acres is the fenced-in lot?

Question

24-10-2023
Mathematics

High School

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A rancher has 14,000 feet of fence and wishes to enclose a rectangular piece of land on his property with a ratio of the length to width of 4:3.

a. What is the width of the fenced-in lot?

b. What is the area enclosed within the fence in square feet?

c. If one square acre is 43,560 square feet, to the nearest thousandth, how many square acres is the fenced-in lot?

Answer :

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bora98585 bora98585 · Answer 1 · 2025-01-18T19:38:32-05:00

Final answer:

To find the width of the fenced-in lot, set up a proportion based on the given ratio. The width of the fenced-in lot is 3000 feet. The area of the fenced-in lot is 12,000,000 square feet. The number of square acres is approximately 275.596 square acres.

Explanation:

To find the width of the fenced-in lot, we can set up a proportion based on the given ratio. Let the width be 3x and the length be 4x. The perimeter of a rectangle is equal to two times the length plus two times the width, so we can set up the equation 2(4x) + 2(3x) = 14000. Solving for x, we find that x = 1000. Therefore, the width of the fenced-in lot is 3000 feet.

To find the area of the fenced-in lot, we can use the formula for the area of a rectangle, which is length times width. Plugging in the values for the length and width, we get 4x * 3x = 12x^2. Substituting x = 1000, we find that the area is 12(1000^2) = 12,000,000 square feet.

To find the number of square acres, we can divide the area in square feet by the number of square feet in one acre, which is 43,560. Dividing 12,000,000 square feet by 43,560 square feet, we get approximately 275.596 square acres.