In this question, I understood the answer that Greg explained which is: If we want to maximize any area we make it a square so 45-45-90 has a bigger area but if we go by the formula lets assume height and base of 30-60-90 triangle is x & root3x and for the 45-45-90 triangle it is x & x so if we compare their areas 30-60-90 one has a bigger area because of root3’s presence however questions also mentions perimeter is same so how does that help in choosing the sides that prove this point?
Hello @Archi , we meet again!
I think what Greg mentioned was the perimeter of both the triangle must be equal
So let’s take 30-60-90 as x + x√3 + 2x = 4.73x
And let’s take 45-45-90 as y + y + y√2 = 3.41y
As you can clearly see x is not equal to y
In a case where you take both perimeters to be equal, 45-45-90 will have a greater area!
right…I chose the numbers so that I make sure parameters are equal in both case and area of the 45-45 one is bigger. Now, that I re-read my question it sounds pretty stupid to me 
Thanks for the help! (again!)