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.