Question

PQRS is a square .N and and M are midpoint of side SR and QR respectively .O is a point on diagnol PR such that OP=OR.show that ONRM is a square.also find the ratio of ar.(NRMO)and ar.(PQRS).

Answer 1

i can only tell the ratio it is pqrs:nrmo
1:4

Answer 2

As PQRS is a square,
RN=RM  -----------------------(1)
As O is the midpoint of PR, RO=OP -----------------(2)
In triangle RNO,(by Pythagoras theorem)
NO=$\sqrt{ OR^{2}- RN^{2} }$
     =OM
THUS all 4 sides are equal
it is a square