Question 223774
The perimeter of a rectangle is 60cm. If the length is decreased by 5 and the width is halved, the perimeter will decrease by 20cm. What are the length and width of the original rectangle?


Step 1.  Perimeter P means adding up all 4 sides of a rectangle.


Step 2.  Let w be the original width.


Step 3.  Let L be the original length.


Step 4.  Let w/2 be the width cut in half


Step 5.  Let L-5 be the length reduced by 5


Step 6.  Then, original perimeter P0=L+L+w+w=2L+2w=60


Step 7.  Then, new perimeter {{{P1=L-5+L-5+w/2+w/2=2L+w-10=60-20=40}}} or {{{2L+w=50}}} after adding 10 to both sides.


Step 8.  Our linear system of equation is given in Steps 6 and 7 as


{{{2L+2w=60}}}

{{{2L+w=50}}}


*[invoke linear_substitution "L", "w", 2, 2, 60, 2, 1, 50 ]




With {{{L=20}}} and {{{w=10}}}.  And {{{P0=2(20+10)=60}}}  and {{{P1= 2*20+10-10=40}}} which are true statements.


Step 5.  ANSWER:  The width is 10 cm and the length is 20 cm.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J