A breeder of horses wants to fence two adjacent rectangle grazing areas along a river with 600 meters of fence.

- write an expression for the total are of the land in terms of the width of the rectangle

Question

A breeder of horses wants to fence two adjacent rectangle grazing areas along a river with 600 meters of fence.

- write an expression for the total are of the land in terms of the width of the rectangle

anonymous · Answer

"Adjacent grazing areas" to me means that they share a fence.  In other words, it's just one big area with a fence in the middle.  I'm going to consider that fence in the middle a width.  The amount of fence we would need is the perimeter (2L + 2W) plus the middle fence (so 2L + 3W instead).  The area of such an area would be L times W

2L + 3w = 600
A = LW
2L = 600 - 3W
L = 300 - (3/2)W

A=(300-1.5W)W=W(300-1.5W)