Question 449238
    Find the length of the side of a square if the length of the diagonal 10. 
Apply Pythagorean theorem:
Let x = length of the side of square
then
{{{x^2 + x^2 = 10^2}}}
{{{x^2 + x^2 = 100}}}
{{{2x^2 = 100}}}
{{{x^2 = 50}}}
{{{x = sqrt(50)}}}
{{{x = sqrt(5*5*2)}}}
{{{x = 5*sqrt(2)}}} (exact answer)
.
{{{x = 7.0711}}} (approx decimal answer)