Question 86703
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/3 = 120/3}}}



==> x = 40



So width = 40 feet.



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



Hope you found the explanation useful.


Warm Regards.


Praseena.