Question

Please help!!! ABCD is a square with diagonals intersecting at E. What is the length of BE

Answer 1

Answer:

$BE = 4\sqrt2$

Step-by-step explanation:

Given

The attached square

Required

Find BE

First, we calculate BD (the diagonal) using Pythagoras theorem.

$BD^2 = BA^2 + AD^2$

Since the shape is a square, then

$BA = AD = 8$

So:

$BD^2 = 8^2 + 8^2$

$BD^2 = 2(8^2)$

Take square roots

$BD = \sqrt{2(8^2)$

$BD = \sqrt{2} * 8$

$BD = 8\sqrt{2}$

BE is half BD.

So:

$BE = \frac{1}{2} * BD$

$BE = \frac{1}{2} * 8\sqrt2$

$BE = 4\sqrt2$