Asquare has side lengths of 9 use the pythagorean theorem to find the length of the diagonal

By drawing a diagonal in a square you are dividing the square into two congruent isosceles right triangles. Using Pythagorean Theorem we can find the length of the diagonal.

a squared + b squared = c squared
a and b represent the sides of the triangle (aka the length of a side of the square), and c represents the hypotenuse (aka the diagonal).
9 squared + 9 squared = c squared
81 + 81 = c squared
162 = c squared
take the square root of both sides
81= x