1. **Stating the problem:** We are given a cuboid with a base rectangle having sides 4 cm and 19 cm, and a diagonal inside the base rectangle measuring 21 cm. We need to verify if these dimensions are consistent or find the missing dimension. 2. **Formula used:** For a rectangle, the diagonal $d$ relates to the sides $a$ and $b$ by the Pythagorean theorem: $$d^2 = a^2 + b^2$$ 3. **Applying the formula:** Here, $a = 4$ cm, $b = 19$ cm, and $d = 21$ cm. Substitute these values: $$21^2 \stackrel{?}{=} 4^2 + 19^2$$ 4. **Calculate each term:** $$21^2 = 441$$ $$4^2 = 16$$ $$19^2 = 361$$ 5. **Sum of squares of sides:** $$16 + 361 = 377$$ 6. **Compare with diagonal squared:** $$441 \neq 377$$ 7. **Conclusion:** The diagonal of 21 cm does not match the diagonal calculated from sides 4 cm and 19 cm. The actual diagonal should be: $$d = \sqrt{4^2 + 19^2} = \sqrt{16 + 361} = \sqrt{377} \approx 19.42 \text{ cm}$$ **Final answer:** The diagonal inside the base rectangle is approximately 19.42 cm, not 21 cm.