Question 201933
Let s = the length of the side of the square, then the length of the diagonal is:
{{{s+2)}}}.
Using the Pythagorean relationship for the sides of a right triangle ({{{c^2 = a^2+b^2}}}) in which c is the diagonal of the square, so:{{{c = s+2}}} and...
{{{(s+2)^2 = s^2+s^2}}} Expand the left side.
{{{s^2+4s+4 = 2*s^2}}} Subtract {{{2*s^2}}} from both sides.
{{{-s^2+4s+4 = 0}}} Use the quadratic formula to solve: {{{s = (-b+-sqrt(b^2-4ac))/2a}}} where: a = -1, b = 4, and c = 4
{{{s = (-4+-sqrt(4^2-4(-1)(4)))/2(-1)}}}
{{{s = (-4+-sqrt(16-(-16)))/(-2)}}}
{{{s = (-4+-sqrt(32))/(-2)}}}
{{{highlight(s = 2+2sqrt(2))}}} or {{{highlight_green(s = 2-2sqrt(2))}}} Discard the negative (green) solution as the length of the side of a square is a positive value (red).
{{{ s = 2+2sqrt(2)}}} This is the exact value of the side of the square.
{{{ s = 4.828}}} This is the approximate value.