4. Solution: Let the length of one right-angle side be x, then the length of the other right-angle side is (8-x) and the area is s..

S= 1/2X(8-X)

= - 1/2x？ +4x

=- 1/2(x-4)？ +8

When x=4, s is the largest.

Therefore, when the lengths of both right angles are 4, the area of the triangle is the largest, and the maximum value is 8.

6. Solution: Let the length of AC be x, then the length of BD is (10-x), and the area of quadrilateral is S.

s=x( 10-x)

= 10x-x？

= - (x？ - 10x)

= - (x-5)？ +25

So when x=5, s is the largest.

Therefore, when AC=5 and BD=5, the area of quadrilateral is the largest.

I want to ask, how did you put the textbook on it?