>>14234591>I couldn't solve this problem for daysDude... this is not that hard. Simply start by figuring out some kind of restriction for the unknown. I did this by realizing the fact that there is an equality between the ratios of lengths and the ratios of surface areas. You know ratios right? Divide the 14 by the 16, so now you have 14/16. The important fact here is that the numerator and denominator in a fraction can be multiplied by the same number or unit without changing the fraction. This should be intuitive because, for example, one liter out of four liters is the same as one inch out of four inches. It's the same number despite the different unit.
Now, imagine that the picture has two overlapping rectangles, one of which is 14 units wide, another 16 units wide. Now, you know the surface area of a rectangle is base times height. The proof of this is pretty trivial and you should be able to figure that out by yourself. So we can multiply the base with a variable 'h' (height) to get surface areas of 14*h and 16*h respectively.
So now, with this knowledge in mind, you can make an equation: 14/16 = (14*h) / (16*h)
Think of the two rectangles again. You can notice that 14*h is the same as 65+? and the 16*h is the same as 91+?. So let's modify the equation to have a restriction on the unknown.
14/16 = (65 + ?) / (91 + ?)
From this point forward it's just basic equation solving which you can just look up somewhere if you don't remember the rules. Turns out this gives only one possible solution for the unknown, ? = 117 which means it must be the right answer.
