# A farmer has 300 feet of fencing and wants to enclose a rectangular corral that borders his barn on one side and then divide it into two plots with a fence parallel to one of the sides. ?

##
Assuming that the farmer will not fence the side along the barn, what are the lengths of the parts of the fence if the total area enclosed is 4800 square feet

Can you please show work thank you

Assuming that the farmer will not fence the side along the barn, what are the lengths of the parts of the fence if the total area enclosed is 4800 square feet

Can you please show work thank you

##### 2 Answers

Each part

#### Explanation:

Two plots of

Three lengths of

Or

Three fences of

Both options give two corrals with a total area of

#### Explanation:

The farmer will have 3 fences of the same length perpendicular to the barn and one length parallel to the barn. It does not matter where he places the middle fence, the area of the total rectangle will be the same.

Let the length of each of the 3 fences perpendicular to the barn

be

The length of the parallel fence will be

The total area enclosed by the fences will be

Putting each factor equal to

Both these options will work for the farmer:

- If the shorter sides (perpendicular to the barn are
#20# feet:

Total rectangle has sides of

The middle fence can be placed anywhere along the longer side.

- If the perpendicular sides are each
#80# feet

The side parallel to the barn will be

Again, the middle fence can be placed anywhere along the side parallel to the barn without affecting the amount of fencing used or the fenced area thus obtained.