Orthohedron Problem: Finding BE When CG = 1/2 HG

Question

Look at the orthohedron in the figure.

$CG=\frac{1}{2}HG$

Calculate $BE$ .

00:00 Calculate BE

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

00:09 Substitute the side value according to the given data

00:13 Each face in the box is a rectangle, therefore opposite sides are equal

00:18 Substitute the side value according to the given data

00:24 Use the Pythagorean theorem in triangle EFB to find EB

00:35 Substitute appropriate values and solve to find BE

00:53 Collect terms and arrange

01:00 Extract the root

01:10 When extracting a root, extract for both numerator and denominator

01:31 Open parentheses properly, make sure to multiply each term

01:39 And this is the solution to the question

$x\frac{\sqrt{5}}{2}+\frac{5\sqrt{5}}{2}$