Let A and B be the two forces
Greatest resultant = A + B = 10 (i)
Least resultant = A - B = 6 (ii)
Solving equations (i) and (ii), we get, A=8 N;B=2 N
When each force is increased by 3N, then
A′=A+3=8+3=11 N,B′=B+3=2+3=5 N.
As the new forces are acting at an angle of 90∘ (i.e.,θ=90∘)
so R′=√A′2+B′2=√(11)2+(5)2=√146 N.