Answer:
55√2 ft
Explanation:
The space diagonal is the root of the sum of the squares of the edge lengths:
√((44 ft)² +(33 ft)² +(55 ft)²) = √(1936 +1089 +3025) ft = √6050 ft
= 55√2 ft
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If you intend 3, 4, and 5, divide the result by 11: 5√2 ft.
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The face diagonal of the 3×4 face will have length 5 (remember the 3-4-5 right triangle?). Then that face diagonal and the edge of length 5 are the legs of a right triangle whose hypotenuse is the space diagonal of interest. Since it is an isosceles right triangle, the hypotenuse length is √2 times the edge length, hence 5√2. (If you intend 44×33×55, multiply these numbers by 11.)