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