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?

Question
Answer 1

No the solid is not a cube.

If it were a cube, the diagonal of the base would be #sqrt2# (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 #sqrt2#, 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 + (sqrt2)^2 = 4^2#
#1 + 2 != 16#
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