Calculate the Face Diagonal of a 5cm Cube Using the Pythagorean Theorem

Question

Shown below is a cube with edges equaling 5 cm.

What is the length of the diagonal on the cube's face?

00:00 Find the diagonal of the cube face

00:03 We'll use the Pythagorean theorem in triangle ABD

00:13 We'll substitute appropriate values and solve to find the diagonal

00:43 And this is the solution to the problem

To solve this problem, we need to determine the length of the diagonal of one face of a cube with edge length 5 cm.

Step 1: Recognize that one face of the cube is a square with side length 5 cm.
Step 2: Apply the Pythagorean theorem formula for the diagonal $d$ of a square, $d = s\sqrt{2}$ , where $s$ is the side length.
Step 3: Substitute $s = 5$ cm into the formula to compute the diagonal.

Now, let's perform the calculations:
The diagonal $d$ of the square (face of the cube) is given by:

$d = 5\sqrt{2}$ .

Therefore, the length of the diagonal on the cube's face is $5\sqrt{2}$ cm.

$5\times\sqrt{2}$ cm