To find the distance between two opposite corners of the floor of the storage unit, we can use the Pythagorean theorem. The storage unit is shaped like a rectangle with a length of 4 meters and a width of 4 meters. The distance between the two opposite corners forms the hypotenuse of a right triangle where the other two sides are the length and the width of the rectangle.
Let the length \(a = 4\) meters and the width \(b = 4\) meters. According to the Pythagorean theorem, the distance \(d\) between the opposite corners is given by:
\[ d = \sqrt{a^2 + b^2} \]
Substituting the values of \(a\) and \(b\):
\[ d = \sqrt{4^2 + 4^2} \] \[ d = \sqrt{16 + 16} \] \[ d = \sqrt{32} \] \[ d = \sqrt{16 \cdot 2} \] \[ d = 4\sqrt{2} \]
Next, we can calculate the numerical value of \(4\sqrt{2}\). Using the approximate value \(\sqrt{2} \approx 1.414\):
\[ d \approx 4 \times 1.414 \approx 5.656 \]
Now, rounding to the nearest tenth:
\[ d \approx 5.7 \text{ meters} \]
Therefore, the distance between two opposite corners of the floor is approximately \(5.7\) meters.
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