A rectangle has length 12 cm and width 8 cm. What is its diagonal?

**The reasoning** When you need the diagonal of a rectangle, think **Pythagoras' Theorem** — the diagonal splits the rectangle into a right-angled triangle. The two sides (length and width) are the two shorter sides, and the diagonal is the hypotenuse. Using the formula: d² = l² + w² d² = 12² + 8² d² = 144 + 64 d² = 208 d = √208 d ≈ **14.42 cm** So the diagonal is approximately 14.42 cm. **Why the wrong options tempt you** - **Option A (4 cm):** You might subtract 12 − 8 = 4. But diagonals are *longer* than sides, not shorter! - **Option B (√208 cm):** This is technically correct but left unsimplified. The question wants the *value*, not the surd form. They gave you 14.42 cm for practicality. - **Option D (20 cm):** Classic trap — you added 12 + 8 instead of using Pythagoras. Addition doesn't work for diagonals! **Quick takeaway** Rectangle diagonal? Always **Pythagoras**: d² = length² + width², then find the square root — and the diagonal is always *longer* than any single side.