Question 213863
The perimeter of a square is 36 centimeters. Find the length of the diagonal.


Step 1.  Let P be the perimeter of a square which means adding up all four sides.


Step 2.  Let s be the side of a square.


Step 3  Then 4s=36 or s=9 centimeters after dividing by 4 to both sides of equation.


Step 4.  Use Pythagorean Theorem to find diagonal which says that the sum of the square of the legs (=s^2+s^2=2s^2) is equal to square of the hypotenuse (diagonal in this case and letting d be the diagonal).


{{{d^2=s^2+s^2=2s^2}}}


{{{d=sqrt(2s^2)}}}


{{{d=sqrt(2*9^2)}}}


{{{d=9*sqrt(2)=12.73}}}


Step 5.  ANSWER:  The length of diagonal is {{{9sqrt(2)=12.73}}} centimeters


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J