Please help! 30 points and crown! A diagonal of a cube measures StartRoot 750 EndRoot cm. The diagonal of a face measures StartRoot 500 EndRoot cm. In centimeters, what is the length of an edge of the cube? Round the answer to the nearest tenth.

? centimeters

Let length, width, and height be s.

Then diagonal of any face would be √( s² + s² ) = √( 2s² )

And we know that it measures  √( 500 ) so that's sufficient for us to figure out the length of an edge of the cube. We do not need to worry about the diagonal of the cube.

Now we have to solve √( 500 ) = √( 2s² )

Square both sides:

500 = 2s²

Divide both sides by 2:

250 = s²

Take the square root of both sides:

√(250) = s ≈ 15.8113883

Rounding to nearest tenth:

s ≈ 15.8

Final 15.8

Hope this helps.