Suppose that there is a cube with edges 12 centimeters in length.Find the length of a diagonal from a lower corner to the diagonally opposite upper corner .

To find the length of the diagonal from a lower corner to the diagonally opposite upper corner of a cube, you can use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the cube forms the hypotenuse of a right-angled triangle, while the two edges of the cube that meet at the lower corner form the other two sides.

Since each edge of the cube has a length of 12 centimeters, the two edges that meet at the lower corner also have a length of 12 centimeters each.

Let's call the length of the diagonal "d."

Applying the Pythagorean theorem, we have the equation:

d^2 = 12^2 + 12^2

d^2 = 144 + 144

d^2 = 288

To find the length of the diagonal, you can take the square root of both sides of the equation:

d = √288

d ≈ 16.97 centimeters

Therefore, the length of the diagonal from a lower corner to the diagonally opposite upper corner of the cube is approximately 16.97 centimeters.