There is this ratio question that I understand the general case, but not for this specific case.
Problem: A rectangle measures 32 cm by 24 cm. Given that its measurements are increased in the ratio 5 : 4 to obtain a second rectangle, find the ratio of their areas.
First, I just want to confirm the meaning of "its measurements are increased in the ratio 5 : 4", does that mean $32+5x$ and $24+4x$ for some $x$? or it means something else?
The solution is 16 : 25.
Looking from the solution, the sentence might mean the ratio of the old to new measurement is 4 : 5.
Then there is a general rule that the ratio of old area to new area is just $old^2 : new^2$ given old is the old measurement and new is the new measurement. Am I correct?
But how can we show it for this specific rectangle in this question. Does that mean the information of length 32 cm and width 24 cm are useless?
In other words, how can we get the solution of 16 : 25 for this problem?
Many many thanks!