9th Class
Mathematics
Quadrilaterals
Question Bank
Quadrilateral
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