Perimeter is 2(a+b) where a and b are length and breadth of the rectangle with area ab. So ab=144 and a+b=25 because 2(a+b)=50. Substitute for b=25-a in ab=144: a(25-a)=144. a^2-25a+144=0 which factorises: (a-9)(a-16)=0.
So the dimensions are 9 and 16.