Question 201750
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+2W}}}


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





{{{308=2L+2W}}} Start with the first equation.



{{{308=2(2W+34)+2W}}} Plug in {{{L=2W+34}}}



{{{308=4W+68+2W}}} Distribute.



{{{308=68+6W}}} Combine like terms on the right side.



{{{0=68+6W-308}}} Subtract {{{308}}} from both sides.



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



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



{{{W=(-240)/(-6)}}} Divide both sides by {{{-6}}} to isolate {{{W}}}.



{{{W=40}}} Reduce.



So the width of the playground is 40 feet.



{{{L=2W+34}}} Go back to the second equation



{{{L=2(40)+34}}} Plug in {{{W=40}}}



{{{L=80+34}}} Multiply



{{{L=114}}} 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.