I’m a bit confused about this question because I initially selected D as my answer. My reasoning was that since the perimeters of the two polygons are not equal, we can’t definitively say that the area of A is greater than B. Additionally, for the right triangle, there don’t seem to be any Pythagorean triplets that satisfy the perimeter condition, so we would need to use decimal values. However, I couldn’t find a combination of side lengths that works. Could you please explain the correct approach to solve this? I would be thankful!
Also, if there already exists solution series for this particular section, could you please let me know where could I find it?
Otherwise, you have to “memorize” the factoid that for a fixed perimeter, the area of a rectangle is maximized when it’s a square. This relates to your question cuz now you know that to maximize QB), you’d consider an isosceles right triangle.
Also, as a tip, don’t rush to choose D just because you don’t know how to solve it. Maybe it helps to think what response a mathematician would give you. For example, you could imagine that amongst all the right triangles subject to a constraint, they’d have some kind of tool to find the case which yields the maximum area. Although a bit silly, that should eliminate your idea of choosing D thus leaving you with better odds.
Thank you! Your answer was spot on. I got the right answer using your method. I just had to consider a case where the area of the right angled triangle would be maximum which would be the case of Isosceles triangle as you correctly pointed out. I didn’t read between the lines and couldn’t understand that I should compare the maximum areas. Should we be following this approach in all the similar area QCs? I understand that this is really subjective and will depend on the question but if you could shed more light on this. it would be helpful because I was trying to find different combinations that would yield 25 as perimeter and it was very tedious.
I mean yeah just like every other QC question, you want to bound each quantity. If the maximum was greater than QA) then the next best thing would’ve been to look at the minimum value and go from there.
There are many such triangles that meet the constraints, so finding the maxima and minima possible area is the first best thing to do. I don’t see what one example would’ve helped you with cuz that still doesn’t help you answer the question definitively/ rigorously.
