SOLUTION: Im working with a perfect cube. The height, width, and length are all represented by the term x. Im trying to find the length of the diagonal from the top corner of the cube to t

Question 605314: Im working with a perfect cube. The height, width, and length are all represented by the term x. Im trying to find the length of the diagonal from the top corner of the cube to the opposite bottom corner of the cube. The dimensions for this triangle is a height of x, a base of x times the sqaure root of 2. I know the diagonal is x times the square root of three. What Im wondering is why, and how do I get that answer.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

In order to get the diagonal of one face you applied the Pythagorean theorem to the triangle formed by two sides on one face and the diagonal on that face. Now create another right triangl where the legs are

and

and use Pythagoras to find the hypotenuse of this triangle which will be your desired diagonal.

John

My calculator said it, I believe it, that settles it

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