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Answer: B.) x = 6

Step-by-step explanation:

Pythagoras Theorem a^2 +b^2 =c^2

Additionally divide 8 by 2 since it's an isosceles triangle and it's in the middle.

[tex]\sqrt{52}[/tex] ^2 - 4^2= x^2

52 - 16 = x^2

x^2 = 36

Square root both sides = 6