Question 222828
The perimeter of a triangle is 51 cm. The lengths of its sides are consecutive odd integers. Find the lengths of all 3 sides.


Step 1.  Perimeter P means adding up all three sides.


Step 2.  Let n be an odd integer.


Step 3.  Let n+2 and n+4 be the next two consecutive odd integers.


Step 4.  Then P=n+n+2+n+4=51.


Step 5.  Solving the equation Step 4 yields the following steps


{{{3n+6=51}}}


Subtract 6 from both sides of the equation


{{{3n+6-6=51-6}}}


{{{3n=45}}}


Divide 45 to both sides of the equation


{{{3n/3=45/3}}}


{{{n=15}}}  Then {{{n+2=17}}} and {{{n+4=19}}}.  Also, P=15+17+19=51 which is a true statement.


Step 6.  ANSWER:  The lengths of the sides are 15 cm , 17 cm and 19 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