SOLUTION: The perimeter of a retectangular playground area is 308 feet. If the lenth of the playground is 34 more feet than twice the width, find the length and width of the playground. to e

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The perimeter of a retectangular playground area is 308 feet. If the lenth of the playground is 34 more feet than twice the width, find the length and width of the playground. to e      Log On


   

Question 201750: The perimeter of a retectangular playground area is 308 feet. If the lenth of the playground is 34 more feet than twice the width, find the length and width of the playground. to ear extra credut, you MUST construct an algebraic equation with a variable and solve using algebra steps.
My solution
P=308 ft L= 2(w+34) 308= 2(60)+ 2L 308=2(60)+2(94)
equaiton: P=2W + 2L 308=120 +2L
308=2w +2w +68 308-120=120-120+2L
308=4w +68 188=2L
308-68=4w +68 -68 188/2=2L/2
240=4w 94=L
240/4=4w/4
60=w
Found 3 solutions by jim_thompson5910, RAY100, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let
L = Length of rectangle
W = Width of rectangle


Since "The perimeter of a retectangular playground area is 308 feet.", this means that 308=2L%2B2W

Also, because "the lenth of the playground is 34 more feet than twice the width", we know that L=2W%2B34




308=2L%2B2W Start with the first equation.


308=2%282W%2B34%29%2B2W Plug in L=2W%2B34


308=4W%2B68%2B2W Distribute.


308=68%2B6W Combine like terms on the right side.


0=68%2B6W-308 Subtract 308 from both sides.


-6W=68-308 Subtract 6W from both sides.


-6W=-240 Combine like terms on the right side.


W=%28-240%29%2F%28-6%29 Divide both sides by -6 to isolate W.


W=40 Reduce.


So the width of the playground is 40 feet.


L=2W%2B34 Go back to the second equation


L=2%2840%29%2B34 Plug in W=40


L=80%2B34 Multiply


L=114 Add


So the length of the playground is 114 feet.


===========================================================

Answer:


So the length and width of the playground are 114 ft and 40 ft respectively.

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter = 2*Length +2 * Width
.
Given, L= 2*W +34
.
P = 2*(2W +34) +2W
.
P = 4W +68 +2W
.
Per = 308,,,,Given
.
308 = 4W +2W +68
.
240 = 6W
.
40 = W,,,,,,,,L=(2w +34)= 2*40 +34 = 114
.
check
P = 2W + 2L = 2(40) + 2(114) = 80 + 228 = 308,,,ok

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

I had a little trouble following what you did until I realized that you have a two-column presentation and the right-hand side is you checking your answer. Once I got the idea of what you were presenting, I can see that you did this one correctly. You did make one slight mis-statement at the very beginning, though you did not allow that error to get into your definition of the equation. You said L = 2(w + 34), when in fact L = w + 34 and 2L = 2(w + 34). Bottom line though, you put it into the equation correctly. Good job.

John