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9514 1404 393
Answer:
√145 ≈ 12.04
Step-by-step explanation:
The length of the space diagonal is the root of the sum of the squares of the prism edge lengths:
d² = a² +b² +c² = 6² +3² +10² = 145
d = √145 ≈ 12.04 . . . inches
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The face diagonal is found using the Pythagorean theorem in the usual way:
f² = a² + b²
The space diagonal is the hypotenuse of the right triangle whose sides are the face diagonal and the remaining edge:
d² = f² +c²
d² = a² +b² +c²
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Here is a diagram.
