1) [tex] NP^{2} =MP ^{2} +MN ^{2} [/tex]
[tex] NP^{2} = 6^{2} +( 2 \sqrt{3} )^{2} [/tex]
[tex] NP^{2}=36+12=48 [/tex]
[tex] NP= \sqrt{48} =4 \sqrt{3} [/tex]
2)[tex] QR^{2} = QP^{2} - PR^{2} [/tex]
[tex] QR^{2} = 24^{2}- 12^{2} [/tex]
[tex] QR^{2} =576-144=432[/tex]
[tex]QR= \sqrt{432} =12 \sqrt{3} [/tex]