john henry will build a rectangular corral using 200 meters of barbed wire. describe the area of the corral are a function of one of its sides

Question

john henry will build a rectangular corral using 200 meters of barbed wire. describe the area of the corral are a function of one of its sides.

Answer 1

We have 2 equations

Area A=L*W

Perimeter P=2L+2W 200=2L+2W Solve this for L L=100-W

This means area can be written as a function of the Width

A=(100-W)*W

Answer 2

Area of a rectangle = Width • Length ⇒ A = W•L

Since there are 200' of wire to form the rectangle, the perimeter = 200.

Perimeter = sum of all sides = Length + Length + Width + Width ⇒ 2•Length + 2•Width = 2L+2W = 200.

2L = 200 - 2W ⇒ L = 100 - W

substituting above we get A = W•(100 - W)

Answer 3

Perimeter = 200 = 2(L+W) = 2L+2W

2L = 200-2W

L = 100-W

Area = LW = (100-W)W = 100W-W^2

A = 100W-W^2