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: $\sqrt{41}$
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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