Calculate CC¹ in an Orthohedron: Given A¹B = 12

Question

Look at the orthohedron in the figure.

$A^1B=12$

Canculate $CC^1$ .

00:00 Find the height of box CC1

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

00:07 Substitute the side value according to the given data

00:12 Each face of the box is a rectangle, therefore all angles are right angles

00:20 Now let's use the Pythagorean theorem in triangle BB1A1 to find BB1

00:28 Let's substitute appropriate values and solve for BB1

00:34 Isolate BB1

00:44 This is the height BB1

00:50 Let's factor 44 into 4 and 11

00:58 Each face of the box is a rectangle, therefore opposite sides are equal

01:04 And this is the solution to the question

$2\sqrt{11}$