Question

PQRS is the square whose diagonals are intersecting at O. If OP = 2cm, then find of length PQ.

Answer 1

If OP =2cm then OQ=2cm as the diagonals are equal and bisect each other.
As, the diagonals are perpendicular to each other, therefore Angle POQ=90°
By Pythagoras theorem,
PQ²=OP²+OQ²
PQ²=2²+2²
PQ²=8
PQ=2√2 cm.

Answer 2

we know square is parellelogram .and all parellelogram have property :-
midpoint of both diagonal are same
hence diagonals of square intersect each other in O
and given OP=2cm
so, PR/2=OP =2cm
PR=4cm
now side length PQ =diagonal PR/root2
=4cm/root2=2root2 cm