Question : Q is a point in the interior of a rectangle ABCD. If QA = 3 cm, QB = 4 cm and QC = 5 cm, then the length of QD (in cm) is:
Option 1: $3\sqrt2$
Option 2: $5\sqrt2$
Option 3: $\sqrt{34}$
Option 4: $\sqrt{41}$
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Correct Answer: $3\sqrt2$
Solution : According to the question, we draw a figure of a rectangle ABCD. Given that: QA = 3 cm, QB = 4 cm and QC = 5 cm QD 2 + QB 2 = QA 2 + QC 2 ⇒ QD 2 + 16 = 9 + 25 ⇒ QD 2 = 34 – 16 = 18 $\therefore$ QD = $\sqrt{18}= 3\sqrt{2}$ cm Hence, the correct answer is $3\sqrt{2}$.
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