Question

A contractor is to build a brick wall 6 feet high to enclose a rectangular garden. Only three sides of the garden need to be enclosed because the fourth side is a building. The owner wants to enclose the maximum area but will only pay for 232 feet of wall. What dimensions should the contractor make the garden

Answer 1

Answer:

Step-by-step explanation:

From the given information:

Since three sides of the garden need to be enclosed because the fourth side is a building.

The area is xy and the perimeter will be x + 2y

Calculating the perimeter in terms of x; we have:

P = x+2y = 232   ----- (21)

y = (232 - x) / 2

y = 116 - (x/2)

Now; to calculate the area since the value of y in terms of x is known.

A = xy

A = x[116 - (x/2)]

A=116x - (x^2/2)  ----- (2)

Taking the derivative of eqaution (2); we have:

A' = 116 - x

Relating it as it is equal to zero, thereby solving for x ; we have:

116 - x = 0

x = 116

From equation (1)

P = 116 +2y = 232

2y = 232 -116

2y = 116

y = 116/2

y = 58

Thus; the area A = xy can be calculated as:

A=xy

A=116(58)

A= 6728