SOLUTION: A square is named ABCD point E lies on side DC. If AB = 16 and AE = 20, find BE.

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Question 1193124: A square is named ABCD point E lies on side
DC. If AB = 16 and AE = 20, find BE.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Diagram:


Focus on triangle ADE
Use the pythagorean theorem to find x.
a%5E2+%2B+b%5E2+=+c%5E2

16%5E2+%2B+x%5E2+=+20%5E2

256+%2B+x%5E2+=+400

x%5E2+=+400-256

x%5E2+=+144

x+=+sqrt%28144%29

x+=+12
Segment DE is 12 units long.
That makes EC = 16 - x = 16-12 = 4 units long.

Now move onto triangle BEC.
We'll use the pythagorean theorem again.
a%5E2+%2B+b%5E2+=+c%5E2

c+=+sqrt%28a%5E2+%2B+b%5E2%29

c+=+sqrt%2816%5E2+%2B+4%5E2%29

c+=+sqrt%28256+%2B+16%29

c+=+sqrt%28272%29

c+=+16.492423
Segment BE is exactly sqrt%28272%29 units long which is approximately 16.492423