solve it

√10²- 6² = Length of QS

$QS=\sqrt{10^2-6^2}=\sqrt{100-36}=\sqrt{64}=$ $\color{#D61F06}\boxed{8}$

PS=12/2=6=2x3. QP=10=2x5, which is similar to a 3:4:5 triangle. Hence, QS=2x4=8. Don't really have to use Pythagoras theorem.

in triangle QPS and QRS QS=QS QP=QR angleQSP=angleQSR by RHS congruency both triangles r congruent by CPCT PS =PR so PS=6cm then by phytagoras theorm we get QS=8cm

Correct Answer is : 8 QS act as the perpendicular bisector of PR PR= 12 So, PS = 6 BY Pythagoras theorm we have = PQ^2= QS^2+PS^2 QS= (10)^2 - (6)^2 = 64 That is = 8x8=64 So, answer is = 8 cm

As we see line QS is a perpendicular bisector. Also line QS is a median though from fig . hence dividing PR into two equal parts as PS and PR .

As Pythagoras theorem is applied on the right angled triangle thus ... taking either tria. QSR or QSP .we can get the ans.

(( lets take QSP triangle for Pythagoras we have to know about all three sides of the triangle .As QR=10 and SR=PR/2 (i.e 6 coz PR is given ) thus simply applying theorem says sq(QR)=sq(QS)+sq(SR) where sq(x)=x*x thus √10²- 6² = Length of QS ))

Just a Pythagoras..