Question 218299
A rectangle has a perimeter of 100 inches.  Its length is (7x + 2) and its width is (5x).  What is the value of x and find the actual measurement of the length and width.  


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


Step 2.  Let the Length L=7x+2 and width w=5x.


Step 3.  Then, {{{P=L+L+w+w=2(L+w)=2(7x+2+5x)=2(12x+2)=24x+4}}}.  Solving yields the following steps.


{{{P=100=24x+4}}}


Subtract 4 from both sides of the equation


{{{100-4=24x+4-4}}}


{{{96=24x}}}}


Divide 4 to both sides of the equation


{{{96/24=24x/24}}}


{{{x=4}}}, {{{L=7x+2=7*4+2=30}}}, w=5x=5*4=20


Check {{{P=2(L+w)=2(30+20)=100}}} which is a true statement.


Step 4.  ANSWER:  The answer is x=4, length is 30 inches and width is 20 inches.


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.


And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV