Question

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

Answer 1

D. 93 x 95; 8835 ft

Explanation:

A rectangle has four sides: 376/4 = 94

94 the average measurement. It is not the exact measurement of each side because a polygon with four side with the same measurement is a square not a rectangle.

So the measure of the rectangles length can be more than 94 and the measure of the width is less than 94. The sum of the length and width should be 188.

Based on the choices. C is not an option. Its the area for a square.

A, B, and D are the remaining options but D has the greatest possible rectangular area.

Answer 2

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