1. **State the problem:** We have two right triangles. The first triangle has legs 14 and 8 units. The second triangle has legs 21 and 12 units, and the hypotenuse is labeled 24 units. We need to verify if the second triangle is a right triangle and compare the triangles. 2. **Calculate the hypotenuse of the first triangle:** Using the Pythagorean theorem, hypotenuse $c = \sqrt{14^2 + 8^2} = \sqrt{196 + 64} = \sqrt{260}$. 3. **Simplify $\sqrt{260}$:** $\sqrt{260} = \sqrt{4 \times 65} = 2\sqrt{65} \approx 16.12$ units. 4. **Check the second triangle's hypotenuse:** Given legs 21 and 12, calculate hypotenuse $c = \sqrt{21^2 + 12^2} = \sqrt{441 + 144} = \sqrt{585}$. 5. **Simplify $\sqrt{585}$:** $\sqrt{585} = \sqrt{9 \times 65} = 3\sqrt{65} \approx 24.19$ units. 6. **Compare given hypotenuse 24 units with calculated $24.19$ units:** The given hypotenuse is approximately correct, slight rounding difference. 7. **Compare the triangles:** The second triangle's sides are exactly $\frac{3}{2}$ times the first triangle's sides (since $14 \times \frac{3}{2} = 21$ and $8 \times \frac{3}{2} = 12$), so the triangles are similar. **Final answers:** - First triangle hypotenuse $\approx 16.12$ units. - Second triangle hypotenuse $\approx 24.19$ units (given as 24 units). - The triangles are similar with a scale factor of $\frac{3}{2}$.