MATH SOLVE

4 months ago

Q:
# 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

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