I have a doubt here. The question says "by the same amount". This phrase can be interpreted in two different ways:

(1) By same amount : same increment. Example, both increase by 10 ft

(2) By same amount : by same percentage. (The the answer differs)

If I consider interpretation (2),

Final_length = Initial_Length * %total_percentage

Final_width = Initial_width * %total_percentage

The %total_percentage =

Let %total_percentage = x

Final_width * Final_length

900

20x * 15x

900

x^2

3

x

x

1.73

Therefore increase in length = (1.73*20 -25)ft = 14.6, which is also a correct answer based on my reasoning.

You cannot work according to the answer, because in a test, you cannot anticipate the correct answer. You have to work for it.