Answer: The correct option is (C) 13 cm.
Step-by-step explanation: As shown in the attached figure below, PR is a diagonal of the cube, PQ is an edge and QR is the diagonal of one of the faces of the cube.
PR = 15 cm and PQ = 15 cm.
We are to find the length of QR.
Since the adjacent faces of a cube are perpendicular to each other, so the triangle PQR will be a right-angled one with ∠PQR = 90° and PR is the hypotenuse.
Therefore, using the Pythagoras theorem, we get
[tex]PQ^2+QR^2=PR^2\\\\\Rightarrow QR^2=PR^2-PQ^2\\\\\Rightarrow QR=\sqrt{15^2-7.5^2}\\\\\Rightarrow QR=\sqrt{225-56.25}\\\\\Rightarrow QR=\sqrt{168.75}\\\\\Rightarrow QR=12.99.[/tex]
That is, QR = 13 cm (rounding to the nearest tenth).
Thus, the length of the diagonal of a face of the cube is 13 cm.
Option (C) is CORRECT.
