Let the length and the breadth of the rectangle be L and B respectively. Given that
Area of rectangle
Perimeter 2
=
1
25
⇒
L×B
(2(L+B))2
=
1
25
⇒25LB=4L2+4B2+8LB =L2+B2=(
17
4
)LB (Note: Alternatively, we can also solve the quadratic equation in terms of L/B and we'd get the same result, i.e. 4 or 1/4) Since B<L, the ratio B:L=1:4