High School Math : How to find the diagonal of a cube

Example Questions

Example Question #1 : Cubes

Find the length of the diagonal connecting opposite corners of a cube with sides of length .

Possible Answers:

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units

units

units

Correct answer:

units

Explanation:

Find the diagonal of one face of the cube using the Pythagorean Theorem applied to a triangle formed by two sides of that face ( and ) and the diagonal itself ():

This diagonal is now the base of a new right triangle (call this ). The height of that triangle is an edge of the cube that runs perpendicular to this diagonal (call this ). The third side of the triangle formed by  and  is a line from one corner of the cube to the other, i.e., the cube's diagonal (call this ). Use the Pythagorean Theorem again with the triangle formed by , and  to find the length of this diagonal.

Example Question #2 : Cubes

Find the length of the diagonal of the following cube:

Possible Answers:

Correct answer:

Explanation:

To find the length of the diagonal, use the formula for a  triangle:

The length of the diagonal is .