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We can find the value of $x$ by checking with the given options.

Consider $\triangle ADE$ using Pythagoras Theorem and put $x=11$

$y^2=(x-3)^2+(DE)^2$, put $y=10$ and after solving we get $DE=6$.

now consider $\triangle BCD$ using Pythagoras theorem $(BD)^2=(BC)^2+(DC)^2$

$\implies (11+6)^2=15^2+8^2$

$\implies 289=289$ which satisfies the condition.

Option (B) is correct.