question_answer

In    the    adjoining    figure    given, \[\angle \mathbf{PQR}=\mathbf{9}{{\mathbf{0}}^{{}^\circ }}\]and QL is a median, \[\mathbf{PQ}=\mathbf{12}\]cm, and \[\mathbf{QR}=\mathbf{14}\]cm. Then, QL is equal to

A)  10cm   

B)  5.5cm

C)  6 cm                           

D)  6.5 cm

Correct Answer: A

Solution :

(a):- Given that, PQ = 5 cm, QR = 12 cm and QL is a median. \[\therefore \]\[PL=LR=\frac{PR}{2}\]                  ???..(I) In \[\Delta PQR,{{\left( PR \right)}^{2}}={{\left( PQ \right)}^{2}}+{{\left( QR \right)}^{2}}\]     (By Pythagoras theorem) \[=144+256\] = 400 \[\Rightarrow \]\[PR=20\] Now, by theorem, If L is the mid-point of the hypotenuse PR of a right angled \[\Delta PQR\], then \[QL=\frac{1}{2}PR=\frac{1}{2}\left( 20 \right)=10cm\]