Question

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

Answer 1

`BE = 4\sqrt2`

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 = √(2) * 8`

`BD = 8√(2)`

BE is half BD.

So:

`BE = (1)/(2) * BD`

`BE = (1)/(2) * 8\sqrt2`

`BE = 4\sqrt2`