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Dear student,

I n ∆ A B C, A p p l y i n g P y t h a g o r a s t h e o r e m A C^{2} = A B^{2} + B C^{2} \Rightarrow A C^{2} = x^{2} + x^{2} \Rightarrow A C^{2} = 2 x^{2} \Rightarrow A C = \sqrt{2} x T h u s, P e r i m e t e r o f ∆ A B C = A B + B C + A C = x + x + \sqrt{2} x = 2 x + \sqrt{2} x = \sqrt{2} x (\sqrt{2} + 1)

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