Question 151984
Ok so far: {{{c^2 = 100}}} and c is the diagonal of the square.
The sides of the square are equal, so when you write: {{{c^2 = a^2+b^2}}} the a and b are equal, so you can write:
{{{c^2 = a^2+a^2}}} or
{{{c^2 = 2a^2}}} Substitute {{{c^2 = 100}}}
{{{100 = 2a^2}}} Divide both sides by 2.
{{{50 = a^2}}} Take the square root of both sides.
{{{sqrt(50) = a}}}
{{{a = sqrt(25*2)}}}
{{{a = sqrt(5^2*2)}}}
{{{a = 5*sqrt(2)}}}
The length of the sides of the square are each exactly {{{5sqrt(2)}}}inches or approximately 7.1 inches.