JAMB - Mathematics (1981 - No. 8)
A cuboid has a diagonal of length 9cm and a square base of side 4cm. What is its height?
9cm
\(\sqrt{65}\)cm
\(4\sqrt{2}\)cm
7cm
6.5cm
설명
Given a cuboid, the diagonal cuts a face of the cuboid into 2 right-angled triangles.
Hence, using the Pythagoras theorem, we have
\(9^{2} = 4^{2} + x^{2}\)
\(81 = 16 + x^{2}\)
\(x^{2} = 81 - 16 = 65\)
\(\therefore x = \sqrt{65} cm\)