169k views
2 votes
The edge length of a cube is 17 cm. Identify the length of its diagonal. Round to the nearest tenth, if necessary. HELP PLEASE!!

User Nsx
by
7.9k points

1 Answer

7 votes

Answer:

29.4 cm

Explanation:

The length of the space diagonal can be found to be the root of the squares of the three orthogonal edge lengths. For a cube, those edge lengths are all the same, so the diagonal length is ...

d = √(17^2 + 17^2 +17^2) = 17√3 ≈ 29.4 . . . . cm

_____

Consider a rectangular prism with edge lengths a, b, c. Then the face diagonal of the face perpendicular to edge "a" has length ...

(face diagonal)^2 = (b^2 +c^2)

and the space diagonal has length ...

(space diagonal)^2 = a^2 + (face diagonal)^2 = a^2 +b^2 +c^2

So, the length of the space diagonal is ...

space diagonal = √(a^2 +b^2 +c^2)

when the prism is a cube, these are all the same (a=b=c). This is the formula we used above.

User Jeremy Salwen
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.