A) 5 cm
B) 5.5 cm
C) 6 cm
D) 6.5 cm
Correct Answer: D
Solution :
Given that, PQ = 5 cm, QR =12 cm and QL is a median, : \[\therefore \] \[PL=LR=\frac{PR}{2}\] In \[\Delta PQR,\] \[{{(PR)}^{2}}={{(PQ)}^{2}}+{{(QR)}^{2}}\] (by Pythagoras theorem) \[={{(5)}^{2}}+{{(12)}^{2}}=25+144=169={{(13)}^{2}}\] \[\Rightarrow \]\[P{{R}^{2}}={{(13)}^{2}}\]\[\Rightarrow \]\[PR=13\] Now, by theorem, if L is the mid-point of the hypotenuse PR of a right angled \[\Delta PQR,\]then \[QL=\frac{1}{2},PR=\frac{1}{2}(13)=6.5\,\,cm\]You need to login to perform this action.
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