This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
we will use the absolute value for the width: $\text{width} = |\sqrt{2}-\sqrt{7}
Here's how to solve the problem:
Assumption: Physical dimensions like length and width must be positive. The given width is negative since and . Therefore, we will use the absolute value for the width: 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 . The length is given
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Here's how to solve the problem: Assumption: Physical dimensions like length and width must be positive.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.