Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem30

11&12 Video Solutions 2010 problem30

Video Transcription

Video Summary

In this problem, the objective is to minimize the combined length of segments drawn from two points, P and Q, on the legs of a right triangle to the hypotenuse. By positioning P and Q together at the right angle, a single perpendicular intersects the hypotenuse, making the points of intersection, K and H, identical. The length of segment KP, which is the height from the right angle to the hypotenuse, is calculated using area relations and the Pythagorean theorem. The minimized expression is 2 times the length of KP, yielding the final answer as \( \frac{2ab}{\sqrt{a^2 + b^2}} \), which corresponds to option C.

Keywords

right triangle

minimize length

hypotenuse intersection

Pythagorean theorem

area relations