SOLUTION: The length of a rectangular playing field is 5 feet less than twice its width. If the perimeter of the playing field is 230 ft, find the length and width of the field.
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Question 85821: The length of a rectangular playing field is 5 feet 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 praseenakos@yahoo.com(507) (Show Source):
You can put this solution on YOUR website! Question:
The length of a rectangular playing field is 5 feet less than twice its width. If the perimeter of the playing field is 230 ft, find the length and width of the field.
Answer:
Perimeter of a rectangle = 2( length + width)
Here length is given in terms of width (that is, length of a rectangular playing field is 5 feet less than twice its width.)
So let us take width = x feet
Twice the width = 2 times the width = 2times x = 2x
Then length = 2x - 5 (because length is 5 feet less that twice the width)
Perimeter = 230 feet (given)
Then by the formula,
2(length + width ) = 230 feet.
2( 2x- 5 + x ) = 230
==> 2( 2x + x - 5 ) = 230
==> 2( 3x - 5 ) = 230
==> 6x - 2 * 5 = 230 ( multiplying 2 with terms inside the parenthisis)
==> 6x -10 = 230
Add 10 to both sides.......
==> 6x - 10 + 10 = 230 + 10
==> 6x = 240
Divide both sides by 6
==>
==> x = 40
That is width = 40 feet
The length = 2x -5 = 2* 40 - 5
==> length = 80 - 5
==> length = 75
Length of the playground = 75 feet and
width of the play ground is 40 feet.
To check your answer, plugg these value in the formula,
perimeter = 2( length + width )
Then you will get the same answer, that is 230 feet,
