The diagram shows a 5 cm x 6 cm x 7 cm cuboid. Calculate the length of the diagonal AB.
4 Give your answer correct to 1 decimal place.
7 cm
1
6 cm
B
5 cm

9514 1404 393

  10.5 cm

Step-by-step explanation:

The length of the space diagonal is the root of the sum of the squares of length, width, and height.

  AB = √(5² +6² +7²) cm = √110 cm ≈ 10.488 cm

  AB ≈ 10.5 cm

The space diagonal is the hypotenuse of the right triangle consisting of an edge (L) and the face diagonal of the face perpendicular to that edge. Of course that face diagonal is the root of the sum of squares of the orthogonal edges: √(W² +H²). So, the space diagonal is ...

  AB = √(L² +(√(W² +H²))²) = √(L² +W² +H²)

step-by-step explanation:

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