Question

The owner of the Rancho Grande has 3,044 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose? shorter side? longer side? what is the area?

Answer 1

Answer:

Step-by-step explanation:

Area of the rectangular piece A = xy

x is the length

y is the width

Perimeter =2x+2y

Given

Perimeter = 3044yds

3044 = 2x+2y

1522 = x+y

x = 1522-y

Substitute into the formula for area

A = xy

A = (1522-y)y

A = 1522y-y²

To maximize the area, dA/dy must be zero

dA/dy = 1522-2y

0 = 1522-2y

2y = 1522

y = 1522/2

y = 761

Since x+y = 1522

X+761 = 1522

X = 761

Dimension is 761yd by 761yd

Area = 761×761 = 579121yd²