SOLUTION: Solve the following word problems. Be sure to show the equation you use for the solution. 44) Geometry. The length of a rectangular playing field is 5 ft less than twice its wid

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Question 86703: Solve the following word problems. Be sure to show the equation you use for the solution.
44) Geometry. The length of a rectangular 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.
Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
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Question:

Solve the following word problems. Be sure to show the equation you use for the solution.
44) Geometry. The length of a rectangular 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.

Answer:

Here length of the ground is given in terms of width....(The length of a rectangular playing field is 5 ft less than twice its width. )

So take, width = x feet.

Twice the width = 2x feet

5 feet less that twice the width = 2x - 5 feet


Length = 2x - 5 feet.


Perimeter = 230 feet( given,

By the formula, perimeter = 2(length + width ) = 230 feet.


==> 2 ( 2x -5 + x ) = 230

Divide through out by 2

==> 2x - 5 + x = 115


==> 2x + x - 5 = 115


==> 3x - 5 = 115


Add 5 to both sides of the equation...


==> 3x - 5 + 5 = 115 + 5


==> 3x = 120

Divide throughout by 3


==> +3x%2F3+=+120%2F3


==> x = 40


So width = 40 feet.


Hence length = 2*40 - 5 = 80 - 5 = 75 feet.


Hope you found the explanation useful.

Warm Regards.

Praseena.