Question 93349
Question: 

John made a rectangular pen for his dog using 28 feet of fencing.
If the width of the pen is 2 feet more than one-half the length, what are the length and width of the pen?


Answer:

Given data:

* Recangular Pen

* 28 feet fencing ==> perimeter of the rectangle is 28 feet.

* width of the pen is 2 feet more than one-half the length.


Let us assume that , length = x feet.


One half of the length = {{{ x/2 }}}


 2 feet more than one-half the length = {{{ x/2 }}} + 2


Therefore, width = {{{ x/2 }}} + 2



Perimeter of the rectangle is given by the formula,


P = 2 (length + width)



==> 28 = 2 ( x + {{{ x/2 }}} + 2 )


Divide throughout the expression by 2


==> 14 = {{{  x +   x/2  + 2  }}}


 Again multiply throughout by 2.


==> {{{ 14*2  =2* x +  2*( x/2)  + 2* 2  }}}



==> {{{ 28 = 2x +x + 4}}}


==> {{{ 28 = 3x + 4}}}


Subtract 4 from both sides....



==> 28 - 4 = 3x + 4 - 4


==> 24 = 3x


Divide both sides by 3



==> {{{ 24/3 = 3x/3 }}}


==> 8 = x


That is length = 8 feet


Therefore, width = {{{ (8/2)+ 2 }}}


==> width 4 + 2 = 6 feet.



Hence the answer.


Hope ypou found the explanation useful.



Regards.


Praseena.