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