Question

A rectangular field is to be bounded by a fence on three sides and by a straight stream on the fourth side. Find the dimensions of the field with the maxiμm area that can be enclosed using 100 feet of fence. Use calculus techniques to solve.

a) Length= 100/4,Width= 100/2
b) Length= 100/2,Width= 100/4
c) Length= 100/3,Width= 100/3
d) Length= 100/4,Width= 100/3
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Answer 1

c

Step-by-step explanation:

Maximum area would be a square with one side the stream....that leaves three sides to use the 100ft of fence , so each would be 100/3

Answer 2

To find the dimensions of the field with the maximum area, we can use calculus techniques. The correct dimensions are Length = 100/4 and Width = 100/3.

Step-by-step explanation:

To find the dimensions of the field with the maximum area that can be enclosed using 100 feet of fence, we can use calculus techniques. Let's assume the length of the rectangle is x feet and the width is y feet. The perimeter of the rectangle is 2(x + y). Since we have 3 sides bounded by the fence, the sum of the lengths of the three sides is 2(x + y). Thus, we have the equation 2(x + y) + y = 100. Simplifying and rearranging the equation, we get y = 100/3 and x = 100/4. Therefore, the dimensions of the field with the maximum area are Length = 100/4 and Width = 100/3. Hence, the correct option is d) Length = 100/4, Width = 100/3.