Question 217533
What is the length of a rectangle that is 6.5 cm wide and has a perimeter of 32 cm?


Step 1.  Perimeter P means adding up all four sides of a rectangle.


Step 2.  Let w be the width and L be the length.


Step 3.  Then {{{P=w+w+L+L=2w+2L=2(w+L)}}}


Step 4.  But w=6.5 and P=32, then 


{{{32=2(6.5+L)=32=13+2L}}}


Subtract 12 from both sides of the equation to get only L terms on the right side.


{{{32-13=13+2L-13}}}


{{{19=2L}}}


Divide by 2 to both sides of the equation


{{{19/2=2L/2}}}


{{{L=19/2=9.5}}}


Check P=2*(6.5+9.5)=2*16=32 which is a true statement.


Step 5.  ANSWER:  The length is 9.5 cm.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J