Find the perimeter, in cm, of the rectangle if 2y=x+2 and x+y+2=2x+1

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Perimeter is measured by taking the four sides of the rectangle and adding them together such that `P=2l + 2b`  where l=length and b=breadth or width.

Working with the given equations, we establish that if `2y = x+2` and `x+y+2=2x+1` where y and x represent the length and breadth on this occasion, we can calculate that from

`2y = x+2` , `therefore 2y-2 = x`  or `x=2y-2 ` and substituting into `P=2x + 2y` :

therefore `P= 2(2y-2) + 2y`

`P= 4y-4+2y`  

`therefore P = 6y-4`

and from `x+y+2=2x+1` , the other given information,substitute the y values for x as already calculated above (`x=2y-2` ) : 

`(2y-2)+ y+2 = 2(2y-2) +1`

`therefore 3y= 4y-4+1` which simplified :

`therefore -y= -3`

`therefore -y=-3`

`therefore y=3`

We also know that `P=6y-4` (from our previous calculations)

`therefore` `P=6(3)-4`

`therefore P=14` cm 


`P=14 cm.` Please note there are various ways to use this information to arrive at the same result.