Question

16. Two medians PS and RT of APQR intersect at Ga
right angles. If PS = 9 cm and RT = 6 cmn, then the
length of RS in cm is
(b) 6
(a) 10
(c) 5
(d) 3​

Answer 1

Answer:     (c)

Therefore PG/GS=2/1=2x/x (since centroid divides each median in the ratio of 2:1)

But PG+GS=PS=9cm

2x+x=9

3x=9

x=3

GS=3cm

Similarly TG/GR=2/1=2y/y

But TG+GR=TR=6

y+2y=6

y=2

GR=2y=2*2=4

Also given that the two medians intersect at right angled ,so angle SGR=90° and so ∆SGR is right angle triangle with GS=3cm,GR=4cm and therefore SR=5cm