What is the maximum area of a right triangle whose legs have a combined length of 10cm?

1/2ab is the area
a+b=10
minus a both sides
b=10-a
sub for b in other equation
1/2a(10-a)=max vol
5a-1/2a²=max vol
take deritivive
5-a=max vol dy/dx
so it is 0 at a=5
it changes from positive to negative slope at a=5
a=5 is the max vol

then
b=10-a
b=10-5
b=5

the area is 1/2*5*5=25/2=12.5 square cm