Resultant is 1. One force is also1. They are perpendicular to each other. This implies angle between p and the 1 force is more than 90. Let us say it is 90 + a.
Resolving p , the one parallel to the 1 force is p sin a, the perpendicular one is p cos a.
Hence both are equal to one.
tan a = 1 hence a = 45. And p = Root of ( 1+1) = root 2.