A diagonal of a cube measures square root of 750 cm. The diagonal of a face measures square root of 500 cm. In centimeters, what is the length of an edge of the cube? Round the answer to the nearest tenth. ____ centimeters

Accepted Solution

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 diagonal of the cube.

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

Square both sides:

500 = 2s²

Divide both sides by 2:

250 = s²

Take square root of both sides:

√(250) = s ≈ 15.8113883

Rounding to nearest tenth:

s ≈ 15.8

Final answer: 15.8

Hope this helps.