justin wants to use 376 ft of fencing to fence off the greatest possible rectangular area for a garden. what dimensions should he use? what will be the area of the graden?A. 92 x 96; 8832ft B. 93 x 95; 8835ft c. 94 x 94; 8836ft d. 89 x 99; 8811ft
Accepted Solution
A:
Let the length be x and the width be y the perimeter of the rectangle will be: 2x+2y=376 thus y=188-x thus the area will be: A(x)=x(188-x) A(x)=188x-x^2
For maximum Area A'(x)=0 from Area we shall have A'(x)=188-2x=0 solving for x we get: x=94 thus the width will be: 188-94=94 thus for maximum area the length=94 ft and width=94 ft Area=94*94=8836 ft^2 thus the answer is: c. 94 x 94; 8836ft