1. **Problem statement:** We have a rectangle with sides 9 cm and 16 cm. We want to find the length of the diagonal $d$. 2. **Formula used:** The diagonal of a rectangle forms a right triangle with the two sides as legs. We use the Pythagorean theorem: $$d^2 = a^2 + b^2$$ where $a$ and $b$ are the side lengths. 3. **Apply the formula:** Substitute $a=9$ and $b=16$: $$d^2 = 9^2 + 16^2$$ $$d^2 = 81 + 256$$ $$d^2 = 337$$ 4. **Find $d$ by taking the square root:** $$d = \sqrt{337}$$ 5. **Simplify the square root if possible:** 337 is not a perfect square and has no perfect square factors, so: $$d \approx 18.36 \text{ cm}$$ 6. **Diagram explanation:** The rectangle can be split into two right triangles by the diagonal $d$. The legs of the triangle are the sides 9 cm and 16 cm, and the diagonal is the hypotenuse. **Diagram:** A right triangle with legs labeled 9 cm (vertical) and 16 cm (horizontal), and the hypotenuse labeled $d$ (the diagonal).