9th Class
Mathematics
Quadrilaterals
Question Bank
Quadrilateral
question_answer
PQRA is a rectangle, \[\mathbf{AP}=\mathbf{24}\]cm. \[\mathbf{PQ}=\mathbf{8}\]cm. \[\Delta \mathbf{ABC}\] is a triangle whose vertices lie on the sides of PQRA such that BQ = 2 cm and \[\mathbf{QC}=\mathbf{18}\]cm. Then the length of the line joining the mid points of the sides AB and BC is
A) \[4\sqrt{2}\]cm.
B) 5 cm
C) 6 cm.
D) 10 cm.
Correct Answer:
B
Solution :
(b): \[QC=18\]cm. \[AC=\sqrt{C{{R}^{2}}+A{{R}^{2}}}=\sqrt{{{6}^{2}}+{{8}^{2}}}=\sqrt{36+64}\] \[=\sqrt{100}=10\]cm. \[BD=DC;\,\,\,BE=EA\] \[\therefore \]\[DE\parallel AC\] and \[DE=\frac{1}{2}AC=\frac{10}{2}=5\].cm