# Given rectangle PQRS with PQ=QR, PQ=SP, and SQ=6√2. Find SR. a)√2. b) 6. c) 5√2 d) not enough information

The rectangle is actually a square. In fact, we have that the side PQ is equal to 2 other sides of the rectangle (QR and SP), and this is possible only if all the 4 sides of the rectangle are equal: this means it is a square. SQ is the diagonal of the square: , but we know that in a square, the diagonal is equal to square root of 2 times the length of the side: where d is the diagonal and L the length of the side. Since in our square the length of the diagonal is , the length of the side must be so, the correct answer is b) 6.

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