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?
By Pythagorean theorem
For minimum length of d, differentiate then equate to zero
Distance of D from side AB for minimum length of d
The same problem was solved by Geometry alone. See the solution here: Distance between projection points