9514 1404 393
Answer:
√3 cm
Step-by-step explanation:
The square of a face diagonal is given by the Pythagorean theorem:
(face diagonal)² = 1² + 1² = 2
Then the square of the space diagonal is ...
(space diagonal)² = 1² +2 = 3
So, the length of the space diagonal is ...
space diagonal = √3 cm
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In the attached diagram, AB and BC are edges of a face of the cube. AC is the diagonal of that face, a "face diagonal." That makes a right triangle with edge CD of the cube. The hypotenuse of that triangle is AD, the "space diagonal". As we have shown, the length of the space diagonal is ...
AD² = CD² +AC² = 1² +(√2)² = 3
AD = √3
