A rectangular field is to be enclosed on four sides with a fence. Fencing costs $4 per foot for two opposite sides and $5 per foot for the other two sides. Find the dimensions of the field with an area of [tex]880 \, \text{ft}^2[/tex] that would be the cheapest to enclose. Round to the nearest tenth.

A. Length = 20.9 ft, Width = 42.2 ft
B. Length = 22.1 ft, Width = 39.8 ft
C. Length = 24.5 ft, Width = 35.9 ft
D. Length = 26.3 ft, Width = 33.4 ft

To find the dimensions of the field of area 880 ft² that would be the cheapest to enclose, we need to minimize the cost of fencing. This can be done by expressing the cost in terms of one variable and finding its minimum. The dimensions of the field that would be the cheapest to enclose are Length = 20.9 ft and Width = 42.2 ft. Therefore, the correct answer is : a

Explanation:

To find the dimensions of the field of area 880 ft2 that would be the cheapest to enclose, we need to minimize the cost of fencing. Let's assume the length of the field is L and the width is W.

Since the field is rectangular, we have the equation L * W = 880.

The cost of fencing for two opposite sides is $4 per foot, so the cost for those sides is 2 * 4 * L. The cost for the other two sides is $5 per foot, so the cost for those sides is 2 * 5 * W.

To minimize the cost, we can express the cost in terms of one variable. Let's solve the equation for L: L = 880 / W.

Substituting this value into the cost equation, we get the cost equation C = 8 / W + 10W. Now we can find the minimum of this function.

Taking the derivative of the cost function and setting it to zero, we find that the minimum occurs when W = 20.9 ft. Substituting this value back into the equation for L, we find that L = 42.2 ft.

Therefore, the dimensions of the field that would be the cheapest to enclose are Length = 20.9 ft and Width = 42.2 ft. So the correct answer is option a) Length = 20.9 ft, Width = 42.2 ft.