A storeowner wants to set up a rectangular display area outside his store. He wi

Question

A storeowner wants to set up a rectangular display area outside his store. He will use one side of the building (which is 45 feet long) as part of one side of the display area. He has 240 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.

Please explain how to work and steps.

A(x)=240x?45

b) A(x)=283x/2

c) A(x)=?x^2+285x/2

d) A(x)=285x/2+x^2

e) A(x)=283x^2/2

Explanation / Answer

The side of the display area opposite the building =x feet

The side of the display area to the building =x-45feet

Let width =y, since perimeter is 240 , set up as

x +x -45 +2y= 240

2x+2y= 240 +45

2x+2y =285

x+y= 285/2

y= 285/2 -x

Now find area as

A=xy

=x(285/2 -x)

=285x/2-x²

A(x)= -x² +285x/2

Looks like, Option C is correct.(not typed clearly )

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