SOLUTION: I am working on a problem that I need some help on. Here it is: Geometry. The length of a rectangle playing field is 5 ft. less than twice its width. If the perimeter of the playi

Algebra ->  Linear-equations -> SOLUTION: I am working on a problem that I need some help on. Here it is: Geometry. The length of a rectangle playing field is 5 ft. less than twice its width. If the perimeter of the playi      Log On


   

Question 112185: I am working on a problem that I need some help on.
Here it is: Geometry. The length of a rectangle 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.
What I have so far is this equation; 2x+2(2x-5)=230?
Am I off to a good start here or not getting it? Thank you for your help.
Barb Neely
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're off to a great start. Now you just need to solve for x




2x%2B2%282x-5%29=230 Start with the given equation



2x%2B4x-10=230 Distribute


6x-10=230 Combine like terms on the left side


6x=230%2B10Add 10 to both sides


6x=240 Combine like terms on the right side


x=%28240%29%2F%286%29 Divide both sides by 6 to isolate x



x=40 Divide

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Answer:
So our answer is x=40

So this means the width is 40. Now take x=40 and plug it into y=2x-5

2%2840%29-5=80-5=75


So the length is 75



Check:

2W%2B2L=P Start with the given perimeter formula


2%2840%29%2B2%2875%29=230 Plug in P=230, W=40, and L=75


80%2B150=230 Multiply


230=230 Add. Since both sides of the equation are equal, our answer is verified.