A water park slide has a rectangular trench and an attached triangular section. Determine the area of the rectangular trench and the hypotenuse of the triangular section.

The problem describes a water park slide with a rectangular trench and an attached triangular section. We need to determine the area of the rectangular trench and the hypotenuse of the triangular section.

Assumptions: Physical dimensions like length, width, base, and height must be positive. Therefore, the width given as $(\sqrt{2} - \sqrt{7})$ meters will be interpreted as its absolute value, $(\sqrt{7} - \sqrt{2})$ meters, since $\sqrt{7} > \sqrt{2}$.

Part 1: Determine the area of the rectangular trench.

Step 1: Determine the length of the rectangular trench, $X$.
The length $X$ is given by the expression:

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