SOLUTION: The length of a rectangular playing field is 5 ft less than twice its width. If the perimeter of the playing field is 230 ft, find the length and width of the field.

Algebra ->  Rectangles -> SOLUTION: The length of a rectangular playing field is 5 ft less than twice its width. If the perimeter of the playing field is 230 ft, find the length and width of the field.       Log On


   

Question 134199: The length of a rectangular playing field is 5 ft less than twice its width. If the perimeter of the playing field is 230 ft, find the length and width of the field.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let L=length, W=width

Since "The length of a rectangular playing field is 5 ft less than twice its width", this means that the first equation is L=2W-5


And our second equation is the perimeter formula:
P=2W%2B2L


230=2W%2B2%282W-5%29 Plug L=2W-5


230=2W%2B4W-10 Distribute


230=6W-10 Combine like terms


240=6W Add 10 to both sides


40=W Divide both sides by 6


W=40


So we know that the width is 40 ft



Now go back to the first equation L=2W-5



L=2%2840%29-5 Plug in W=40


L=75 Simplify


So the length is 75 ft