Calculate Length BB₁: 3D Box Geometry with Given Distance 18

Question

Calculate the length of $BB_1$ in the box shown in the diagram.

00:00 Find BB1

00:03 Each face in the box is a rectangle, therefore opposite sides are equal

00:09 Let's substitute the side value according to the given data

00:16 Each face in the box is a rectangle, therefore all angles are right angles

00:23 Now we'll use the Pythagorean theorem in triangle A1D1D to find DD1

00:37 Let's substitute appropriate values and solve for DD1

00:44 Isolate DD1

00:52 This is the height DD1

00:59 Each face in the box is a rectangle, therefore opposite sides are equal

01:05 And this is the solution to the question

$\sqrt{324-a^2}$