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Goshia [24]
3 years ago
6

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

Mathematics
1 answer:
Snezhnost [94]3 years ago
8 0

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

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