perplexus.info :: Geometry : Area of an Obtuse triangle from Equilateral triangle

Area of an Obtuse triangle from Equilateral triangle (Posted on 2023-09-08)

In Obtuse triangle from equilateral triangle we were asked to construct an 120-degree obtuse triangle from segments of an equilateral triangle ABC and an arbitrary cevian BD.

What is the area of this 120-degree obtuse triangle expressed in terms of the lengths of side AB and cevian BD?

No Solution Yet Submitted by Brian Smith

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Solution

Comment 1 of 1

Using your geometric solution to name the extra points (which is essentially how I solved this problem when I came across it.)

[DFC] = 2*[ABC] - [ABD] - [DBF] - [FBE]

triangle FBE is congruent to triangle DBC, so [ABD]+[FBE]=[ABC]

[DFC] = [ABC] - [DBF]

these are both equilateral so the area is simply

[DFC] = sqrt(3)/4 ((AB)^2-(BD)^2)

Posted by Jer on 2023-09-09 11:40:22

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info