Question 215349
The perimeter of a square is 20 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=20, then {{{c=20sqrt(2)/4=5sqrt(2)}}} or {{{c=7.07}}} cm


Step 4.  The diagonal is 7.07 cm.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J