Assumption: Physical dimensions like length and width must be positive. The given width (sqrt(2)-sqrt(7)) is negative since sqrt(2) ~= 1.414 and sqrt(7) ~= 2.646. Therefore, we w

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Assumption: Physical dimensions like length and width must be positive. The given width $(\sqrt{2}-\sqrt{7})$ is negative since $\sqrt{2} \approx 1.414$ and $\sqrt{7} \approx 2.646$. Therefore, we will use the absolute value for the width: $\text{width} = |\sqrt{2}-\sqrt{7}| = \sqrt{7}-\sqrt{2}$ meters.
Assumption: The triangular section is a right-angled triangle, as the term "hypotenuse" is used.

a) Determine the area of the rectangular trench

Step 1: Simplify the expression for $X$.
The length $X$ is given