## Distance between projection points on the legs of right triangle (solution by Calculus)

**Problem**

From the right triangle *ABC* shown below, *AB* = 40 cm and *BC* = 30 cm. Points *E* and *F* are projections of point *D* from hypotenuse *AC* to the perpendicular legs *AB* and *BC*, respectively. How far is *D* from *AB* so that length *EF* is minimal?