From the diagram, find the value of x.

The image shows a rectangle. The diagonal of a rectangle forms a right-angled triangle with two adjacent sides. The sides of this triangle are the length of the rectangle (60), the width of the rectangle (x), and the diagonal (61).

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).
Let $a = 60$, $b = x$, and $c = 61$.
The formula is $a^2 + b^2 = c^2$.

Subtract 3600 from both sides of the equation.

Take the square root of both sides.

The value of x is 11.