Question 134800
The diagonal of a square forms an isoceles right triangle with two of the sides.  Using Pythagoras, and remembering that the legs of the triangle are the same length, we have {{{c=8sqrt(2)}}}, and since {{{a=b}}}, {{{a^2+b^2=a^2+a^2=2a^2}}}.  That means:


{{{2a^2=(8sqrt(2))^2}}}


{{{2a^2=64(2)}}}


{{{a^2=64}}}


{{{a=8}}}