1. **Stating the problem:** We have a right triangular prism shaped ramp with dimensions: base length $20$ ft, vertical height $12$ ft, side height $8.5$ ft, and diagonal ramp length $21.7$ ft. We want to understand the relationships between these dimensions and verify the ramp's geometry. 2. **Formula and rules:** For a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse. 3. **Applying the Pythagorean theorem:** The ramp's diagonal length $21.7$ ft should satisfy $$8.5^2 + 20^2 = ?$$ Calculate: $$8.5^2 = 72.25$$ $$20^2 = 400$$ Sum: $$72.25 + 400 = 472.25$$ 4. **Compare with diagonal squared:** $$21.7^2 = 470.89$$ 5. **Interpretation:** The calculated sum $472.25$ is very close to $470.89$, indicating the diagonal length $21.7$ ft is consistent with the base and side heights within rounding error. 6. **Vertical height check:** The vertical height $12$ ft is perpendicular to the base and side, forming the prism's height, not part of the right triangle base. **Final conclusion:** The ramp's dimensions satisfy the Pythagorean theorem for the triangular base, confirming the geometry is consistent.