A cuboid has a diagonal of length 9cm and a square base of side 4cm. What is its height?
-
A.
9cm -
B.
(sqrt{65})cm -
C.
(4sqrt{2})cm -
D.
7cm -
E.
6.5cm
Correct Answer: Option B
Explanation
Given a cuboid, the diagonal cuts a face of the cuboid into 2 right-angled triangles.
Hence, using the Pythagoras theorem, we have
(9^{2} = 4^{2} + x^{2})
(81 = 16 + x^{2})
(x^{2} = 81 – 16 = 65)
(therefore x = sqrt{65} cm)