Calculate BB¹ in a Rectangular Prism with Diagonal Length 2√14 cm

Question

Look at the rectangular prism in the figure below.

The length of the diagonal is $2\sqrt{14}$ cm.

Calculate $BB^1$ .

00:00 Find the height of box BB1

00:03 Let's draw the diagonal of the base face

00:08 Use Pythagorean theorem in triangle A1B1C1 to find A1C1

00:11 Substitute appropriate values according to the given data and solve for the diagonal

00:19 This is the size of the diagonal in the square

00:28 Right angle between box diagonal and face

00:35 Now use Pythagorean theorem in triangle A1C1C to find CC1

00:42 Substitute appropriate values and solve for CC1

00:51 Isolate CC1

01:05 This is the height CC1

01:08 Each face in the box is a rectangle, therefore opposite sides are equal

01:12 And this is the solution to the question

$2$