What is the function that represents its length in terms of the width?

Question

Jim and his dad are building a rectangular flower bed. They have a total of 35 feet of landscaping timber to use, and they want to use all of it. They are not sure what width and length they want the flower bed to be. The perimeter of the rectangle is given by the equation 2l + 2w = p.
Jim and his dad want to find the length of the garden once they decide its width. I need to use function notation to write a function that represents its length in terms of the width.

Answer 1

Hi Johnny,

 

When the problem asks for a function of a term, that will be what the rest of the equation is equal to, so you'll need to rearrange the equation to have that term alone on one side.  In this case, you want a function of length in terms of width, meaning L = equation with w variables in it.  

 

In your base perimeter equation, you have 3 variables, L, w, and p.  Your problem tells you the amount of timber you have (35 feet), which will replace p in your equation so you have:

 

2L + 2w = 35

 

You want to now get L by itself, so you'll move the 2w term over by subtracting it:

 

2L + 2w = 35

    - 2w    -2w

2L          = 35 - 2w

 

Now that you have just L variables one side, you're almost done.  Since L has a coefficient though, you need to get rid of it by dividing both sides by 2 so you get:

 

2L/2 = (35 - 2w)/2

 

Which will simplify into:

 

L = 35/2 -2w/2  

L = 17.5 - w