Express the area of the sidewalk as a function of x.

Question

A garden is in the shape of a rectangle. A sidewalk of width 5 ft surrounds the garden. One side of the garden has length 20 ft. The other side has length x. Express the area of the sidewalk as a function of x.

Answer 1

Hi Aleses,

 

Let's set up this problem.

 

The rectangular garden is 20' by x'; the area is 20x

There is a sidewalk around the garden that is 5 feet wide.

 

So the total area of the garden and the sidewalk is

(20+10) (x+10)

I've added 10 to each dimension since there would be a 5' sidewalk on each side.

 

This equals 30(x+10) = 30x+300

 

The area of the sidewalk alone is the area of the garden and sidewalk minus the area of the garden alone.

 

30x + 300 - 20x = 10x+300