Question

You have 1000 feet of fencing to enclose a rectangular region and subdivide it into three smaller rectangular regions by placing two fences parallel to one of the sides (see picture). Express the area of the enclosed rectangular region, A, as a function of one of its dimensions, x.

Answer 1

`A = 250 b - (1)/(2) {b}^(2)`

Explanation:

let h be the lenght of one of the sides of the rectangle and b the other.

to enclose the rectangular region we will need

2h+2b feet of fencing.

then to make the divitions we will need two more pieces of the lenght of one side. if we supose the divitions are parallel to side h, then we will need 2h feet more.

if 2h+2b+2h is the total amount of feet of fencing we need then

4h+2b=1000

4h=1000-2b

h=(1000-2b)/4

h=1000/4-2b/4

h= 250 - 1/2 b

to calculate the area of a rectagle we have

A=bxh

then

A=b (250 - 1/2 b)

A=250b - 1/2 b^2