Question 1193124
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Diagram:
<img src = "https://i.imgur.com/L5sOugJ.png">


Focus on triangle ADE
Use the pythagorean theorem to find x.
{{{a^2 + b^2 = c^2}}}


{{{16^2 + x^2 = 20^2}}}


{{{256 + x^2 = 400}}}


{{{x^2 = 400-256}}}


{{{x^2 = 144}}}


{{{x = sqrt(144)}}}


{{{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^2 + b^2 = c^2}}}


{{{c = sqrt(a^2 + b^2)}}}


{{{c = sqrt(16^2 + 4^2)}}}


{{{c = sqrt(256 + 16)}}}


{{{c = sqrt(272)}}}


{{{c = 16.492423}}}
Segment BE is exactly {{{sqrt(272)}}} units long which is approximately 16.492423
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