Question 64251: 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 by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! 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
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