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

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)   (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

Also, because "the lenth of the playground is 34 more feet than twice the width", we know that

Start with the first equation.

Plug in

Distribute.

Combine like terms on the right side.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the width of the playground is 40 feet.

Go back to the second equation

Plug in

Multiply

Add

So the length of the playground is 114 feet.

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Answer:

So the length and width of the playground are 114 ft and 40 ft respectively.
Answer by RAY100(1637)   (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)   (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

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