Question 64251
QUESTION:


The perimeter of a rectangle is 76 meters.  the length is 16 meters less than twice the width.  find the length of the rectangle.


ANSWER:


Perimeter of a rectangle is given by the formula,


 P = 2 ( length + width)


That is ,

P = 2 ( L + W ) -----------------------(1)


Here we have,


P = 76 meters.


Length is given as 16 meters less than twice the width( that is lenth is given in terms of width)

So let's take,


W = x meters.


Twice of width = 2*x = 2x meters.


So we can take length as,


L = (2x - 16) meters



Now substitute all these values in equation (1)



==> 76 = 2 ( 2x - 16 + x )



==> 76 = 2 ( 2x + x -16)


==> 76 = 2 ( 3x -16 )


Now divide both sides of the equation by 2 


==> 76/2 = { 2 ( 3x -16 )}/2



==> 38  = 3x - 16


Add 16 to both sides,


==> 38 + 16 = 3x -16 + 16


==> 54 = 3x


Now again divide both sides by 3


==> 54/3 = 3x/3



==> 18 = x


Thus we got the value of x which is the width of the rectangle.


W = 18 meters


==>  L = 2x - 16  =  2*18 - 16  =  36 - 16  =  20 meters.



So length of the rectangle is 20 meters.



You can check  your answer by giving values of L and W in  equation (1) and find whether is is equal to 76 or not.


Hope you understood.



Regards.


praseenakos@yahoo.co.in