Question 85821
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



==> {{{ 6x/6 = 240/6 }}}



==> 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,




Hope you found the explanation useful....




Regards.



Praseena.