ΔPQR is an isoceles triangle and ∠PQR=90°, In right angle ΔPQR, by Pythagoras theorem ⇒ PR2=PQ2+QR2 ⇒ PR2=(10)2+(10)2(∵PQ=QR=10cm) ⇒ PR2=200 ⇒ PR=√200=10√2cm Now, we know, that perpendicular in an isosceles triangle bisect the third side. ∴ QL is perpendicular to PR. ∴ LR=
10√2
2
=5√2cm Now, in right angle ΔQLR, by Pythagoras theorem. ⇒ QL2=QR2−LR2 ⇒ QL2=(10)2−(5√2)2 ⇒ QL2=100−50 ⇒ QL2=50 QL=√50=5√2cm