Answer:

a/b = 22/143

Step-by-step explanation:

Let a/b = 2/13;     a = numerator;      b = denominator

from a/b = 2/13;        b=13a/2 ------ eq. 1

Lets define the equation from the problem

4(b-a) = a^2 ------ eq. 2

Substitute eq. 1 to eq. 2

4[(13a/2) - a] = a^2

Distribute 4 into the bracket

26a - 4a = a^2

22a = a^2 (simplify a)

22 = a (numerator)

substitute the value of a to eq. 1

b = 13(22) / 2

b = 143

Lets do the checking using the eq. 2

4(b - a) = a^2

4(143 - 22) = (22)^2

484 = 484