question_answer

Q is a point in the interior of a rectangle ABCD. If \[\mathbf{QA}=\mathbf{4}\]cm, \[QB=3\]cm and \[\mathbf{QC}=\mathbf{5}\] cm, then the length of QD (in cm) is

A)  \[4\sqrt{2}\]

B)  \[5\sqrt{2}\]

C)  \[\sqrt{34}\]                             

D)  \[\sqrt{41}\]

Correct Answer: A

Solution :

(a): Using Pythagoras theorem, \[Q{{D}^{2}}+Q{{B}^{2}}=Q{{A}^{2}}+Q{{C}^{2}}\] \[\Rightarrow \] \[Q{{D}^{2}}+9=16+25\] \[\Rightarrow \] \[Q{{D}^{2}}=41-9=32\] \[\Rightarrow \] \[QD=\sqrt{32}=4\sqrt{2}\] cm