Answer:
[tex]BE = 4\sqrt2[/tex]
Step-by-step explanation:
Given
The attached square
Required
Find BE
First, we calculate BD (the diagonal) using Pythagoras theorem.
[tex]BD^2 = BA^2 + AD^2[/tex]
Since the shape is a square, then
[tex]BA = AD = 8[/tex]
So:
[tex]BD^2 = 8^2 + 8^2[/tex]
[tex]BD^2 = 2(8^2)[/tex]
Take square roots
[tex]BD = \sqrt{2(8^2)[/tex]
[tex]BD = \sqrt{2} * 8[/tex]
[tex]BD = 8\sqrt{2}[/tex]
BE is half BD.
So:
[tex]BE = \frac{1}{2} * BD[/tex]
[tex]BE = \frac{1}{2} * 8\sqrt2[/tex]
[tex]BE = 4\sqrt2[/tex]
