# A clear plastic prism has six faces, each of which is a parallelogram of side length 1 meter. A diagonal made of nylon filament line connecting two opposite vertices of the solid has a length of 4 meters. ls the solid a cube?

Dec 10, 2016

No the solid is not a cube.

#### Explanation:

If it were a cube, the diagonal of the base would be $\sqrt{2}$ (found using the Pythagorean theorem

${a}^{2} + {b}^{2} = {c}^{2}$,

where $a$ and $b$ are both equal to $1$ meter.

You now use a different right triangle to find the diagonal from opposite vertices, the diagonal of the base is $\sqrt{2}$, the height is $1$ (if it is a cube), and the hypotenuse is the diagonal from opposite vertices.

Again, use ${a}^{2} + {b}^{2} = {c}^{2}$

${1}^{2} + {\left(\sqrt{2}\right)}^{2} = {4}^{2}$

$1 + 2 \ne 16$