Question 213090
Find the length of a side of a square, given the following lengths of a diagonal 10 


Step 1.  Use the Pythagorean Theorem:  Sum of the squares of the sides equals to the square of the hypotenuse.   In this case the diagonal is the hypotenuse. 


Step 2.  Let s be the side of the square and let d be the diagonal of length 10.


Step 3.  So the equation is the following and is solved as follows.


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


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


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


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


{{{d/sqrt(2)=s*sqrt(2)/sqrt(2)}}}


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


{{{s=10/sqrt(2)}}}


{{{s=7.071}}}


Step 2.  The side of the square has length 7.071.



I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J