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Farmer Jack wants to build a fence that is 44 feet long with an area greater than 105 square feet for a chicken coop. Under which conditions should Farmer Jack build his fence?
A. The length of the fence must lie between 7 ft. and 15 ft., including 7 ft. and 15 ft.
B. The length of the fence must be greater than or equal to 15 ft. or less than or equal to 7 ft.
C. The length of the fence must be greater than 15 ft. or less than 7 ft.
D. The length of the fence must lie between 7 ft. and 15 ft., not including 7 ft. and 15 ft.

Respuesta :

The conditions under which the Farmer Jack should build his fence is; B. The length of the fence must be greater than or equal to 15 ft. or less than or equal to 7 ft.

How to find the area of a fence?

We are told that the length of the entire fence is 44 ft long. Thus it means that the perimeter is 44 ft long.

Now, since the fence is a rectangular shape, it means that;

a + b = 44/2

a + b = 22  ----(1)

Now, we are told that the area has to be greater than 105 sq. ft. Thus;

ab > 105    ------(2)

From eq 2; a > 105/b

Thus; (105/b) + b = 22

Multiply through by b to get;

105 + b² = 22b

b² - 22b + 105 = 0

Solving using quadratic equation calculator gives;

b  ≤ 7 or b ≥ 15

Thus, we can conclude that the length of the fence must be greater than or equal to 15 ft. or less than or equal to 7 ft.

Read more about Fence Area at; https://brainly.com/question/15242796

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