On an open space at right angle ▲ABC, design a DEBF-shaped garden with an inscribed distance (all vertices of the distance are above ▲ABC). If ∠ ABC = 90, AB = 30. BC=40 Known, determine the position of point D to maximize the garden area, and find the maximum area.

Analysis: let d be on the hypotenuse AC, e and f be on BC and AB, and da = X.

∫∠ABC = 90°，AB = 30。 bc=40,∴tana=4/3==>； Sina =4/5, cosA=3/5.

DF=xsinA，BF=30-xcosA

s=df*bf=(xsina)*(30-xcosa)=24x- 12/25x^2=- 12/25(x-25)^2+300

∴ When AD=25, the maximum s is 300.