Question 215356
The perimeter of a square is 36 cm. Find the length of the diagonal.


Step 1.  We'll use the Pythagorean Theorem which states that the sum of the  square of the sides or legs of a right triangle is equal to the square of the hypotenuse or {{{c^2=a^2+b^2}}} and for this example, c is the diagonal and a=b is the side since it's a square.


Step 2.  So with a=b then {{{c^2=a^2+a^2=2a^2}}} or c=a*sqrt(2) and {{{a=c/sqrt(2)}}}


Step 3.  Perimeter P means that we add up all the form sides or {{{P=4a=4c/sqrt(2)}}} or {{{c=P*sqrt(2)/4}}}.  If P=36, then {{{c=36sqrt(2)/4=9sqrt(2)}}} or {{{c=12.73}}} cm


Step 4.  The diagonal is 12.73 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