Math Is Fun Forum

MD Muzibur Rahman

Member

Registered: 2014-05-21

Posts: 4

Contructing a triangle

Length of three perpendiculars from three heads on the three arms of a triangle is given. How to construct that triangle?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Contructing a triangle

hi MD Muzibur Rahman

Welcome to the forum.

At the moment I cannot see a solution to this, but I'll work on it.  Here's my thinking so far:

Let's say the sides are a, b and c; and the perpendiculars are h, i and j.

Because the area of the triangle is fixed we know that ah = bi = cj so dividing by hij gives

So it looks like you can find a way to get a, b and c from the known h, i and j.  {Maybe the sine rule?)

More when I've got it 'sorted'.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Contructing a triangle

I've come up with this method, which is rather clumsy but does work.

I'll show with an example.

Say h = 6, I = 8 and j = 5.

Then

Choose a = 20 (say)  => b = 15 and c = 24

Construct that triangle and find the 'h' for that triangle.  I got 14.95.

G is the intersection of the altitudes.  Make G the centre of a dilation (enlargement) with scale factor 6/14.95

Construct the new triangle.  It has the required properties.  Here it is:

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob