Trapezoid Divided into Equal Areas

by a Line Parallel to the Bases  -  The Root Mean Squared (RMS)


Given an isosceles trapezoid with parallel sides of length a and b.

A line of length c is drawn parallel to the bases of length a and b so as to divide the isosceles trapezoid into two equal areas.

Express c in terms of a and b.

See EMAT 4600/6600 problem Lines Parallel to the Bases of a Trapezoid.

This is the solution to the fourth part of that problem.  It corresponds to the Root Mean Squared (RMS)



For a construction of the segment of length c, click here.

For GSP file of the completed construction, click here



Prove that for positive a and b,

with equality if and only if a = b.

Return to the EMAT 4600/6600 Page.