Square Inscribed on Any Base of a Triangle


Take any triangle ABC.

Problem 1.

Develop a ruler and compass construction for inscribing a square in a triangle with one side along a specified base.

Help? See Squares Inscribed in a Right Triangle.

Problem 2.

Given the inscribed square as indicated in the drawing, find an expression for s in terms of h and a.


More Help?

GSP Sketch?

This result shows that the length of the side of a square inscribed on a given base of a triangle is one half the harmonic mean of the altitude to that base and the base.

Another way to set it up.


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