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?

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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?

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Answer 1 · 2016-12-10T16:21:04

No the solid is not a cube.

Explanation:

If it were a cube, the diagonal of the base would be $\sqrt{2}$ $sqrt2$ (found using the Pythagorean theorem

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

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

You now use a different right triangle to find the diagonal from opposite vertices, the diagonal of the base is $\sqrt{2}$ $sqrt2$ , the height is $1$ $1$ (if it is a cube), and the hypotenuse is the diagonal from opposite vertices.

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

$1^{2} + {(\sqrt{2})}^{2} = 4^{2}$ $1^2 + (sqrt2)^2 = 4^2$

$1 + 2 \neq 16$ $1 + 2 != 16$

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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?

1 Answer

Explanation:

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