Question

A storeowner wants to set up a rectangular display area outside his store. He will use one side of the building (which is 25 feet long) as part of one side of the display area. He has 190 linear feet of fencing material to use to fence in the display area. Write a function which expresses the total area of the display area in terms of the length x of the side of the display area opposite the building.

Answer 1

`A=(215*x)/(2)-x^2)`

Explanation:

From the question we are told that:

Total length of building side
`x=25feet`

Perimeter of fence in
`P=190feet`

Generally the perimeter of the display area is given as mathematically given by

`2L+2B=P+x\\2L+2B=190+25`

Therefore

`2L+2B=215`

`L+B=(215)/(2)`

`B=(215)/(2)-L`

Generally the Area of the display area A is given as mathematically given by

`Area A=L*B`

`Area A=L*((215)/(2)-L)`

`Area A=(215*L)/(2)-L^2)`

Length L in terms of x

`Area A=(215*x)/(2)-x^2)`