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In the figure shown, what is the value of x?

(1) a = b = 4

If a = b = 4, PQRS has to be a square. Here, RS = 4.

But, we have no idea about the length of TR

(Insufficient)

(2) \(c = 4\sqrt{2}\)

With the information c = \(4\sqrt{2}\), we can't determine

the value of TR. Also, we have no information about RS

(Insufficient)When we combine the information from both the statements,

PR = 4(because PR is the side of a square) and the right triangle

has to be an isosceles right-angled triangle. Therefore, TR = \(4\sqrt{2}\)

The value of x = RS + TR = 4 + \(4\sqrt{2}\)

(Sufficient - Option C)
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