Areas in Triangle II

Here's a problem very much related to a better known one. Given a triangle, extend each side by its own length in one direction following a certain order. Connect the newly obtained points. Prove that the area of the big triangle is 7 times that of the given one.


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

Of course, we can add 1, 2, 3, or, in general, N lengths to each side. The triangles so obtained have areas 7, 19, 37, or, in general, 3N2 + 3N + 1 times greater than the given triangle. (This this #A003215 in the On-Line Encyclopedia of Integer Sequences.)

|Activities| |Contact| |Front page| |Contents| |Did you know?| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny

 63029955

Search by google: