Question

this diagram shows a cube. each edge of the cube is 6 units long. the diagonal of each face is x units long. the diagonal of the cube is y units long. find x and y. if necessary, round your answers to the nearest tenth. x = units y = units

Explanation:

Step1: Find the value of x

Use the Pythagorean theorem on the face of the cube. The two - side lengths of the right - triangle on the face are both 6 units.
$x=\sqrt{6^{2}+6^{2}}=\sqrt{36 + 36}=\sqrt{72}=6\sqrt{2}\approx8.5$

Step2: Find the value of y

Use the Pythagorean theorem in the three - dimensional space of the cube. One side is 6 units and the other side is x ($x = 6\sqrt{2}$ units).
$y=\sqrt{(6\sqrt{2})^{2}+6^{2}}=\sqrt{72 + 36}=\sqrt{108}=6\sqrt{3}\approx10.4$

Answer:

$x\approx8.5$ units
$y\approx10.4$ units