Question 324505
If you draw a square with side length 'x' and cut it down the diagonal, you will create two triangles. So if you can find the hypotenuse of either triangle, they you have found the diagonal. We can find the hypotenuse 'h' by the pythagorean theorem {{{a^2+b^2=c^2}}}. In this case, {{{a=b=x}}} and {{{c=h}}} which means that {{{x^2+x^2=h^2}}}. Solve for 'h' to get {{{h=x*sqrt(2)}}} (note: we're only considering the positive square root).



So if you have a side length 'x', you can use it to find the hypotenuse 'h' by the formula {{{h=x*sqrt(2)}}}



So for "a 9 ft square", we have x=9 which makes the diagonal to be {{{h=9*sqrt(2)= 12.7279221}}} ft (approximately)