Understanding the Relationship

* A square's diagonal divides it into two right-angled triangles.

* The diagonal is the hypotenuse of these triangles.

* We can use the Pythagorean theorem to find the diagonal's length.

Pythagorean Theorem

* a² + b² = c²

* Where 'a' and 'b' are the sides of the square, and 'c' is the diagonal (hypotenuse).

Calculation

1. Substitute: a = 5 inches, b = 5 inches

2. Equation: 5² + 5² = c²

3. Solve: 25 + 25 = c²

50 = c²

c = √50

c ≈ 7.07 inches

Answer: The length of the diagonal of a square with a side of 5 inches is approximately 7.07 inches.