Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

line

6x + 8y = 48 intersects the coordinate axis at A and B respectively.
a line L bisects the area and the perimeter of the triangle AOB.
where O is the origin. the number of such lines possible is

actually i did not understand meaning of that line

a line L bisects the area and the perimeter of the triangle AOB.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: line

hi

see diagram 1

Also tried to find such a line.  diagram 2.

Suggestion:

Call P (0 , y) and Q (x , 6 - 0.75x)

Form equations for the perimeter and area constraints.

I suspect there is a unique solution.

Then repeat with P on the x axis for maybe a second solution.

That's only a guess at this stage.

Bob

Last edited by Bob (2012-01-10 00:20:36)

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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

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: line

thanks bob

i am trying using your figure

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: line

It occurs to me that there are probably three answers.

(i) Q on AB.  P on y axis.

(ii) Q on AB. P on x axis.

(iii) P on x axis.  Q on y axis.

Bob.

I have a proof for the inscribed circle problem.  I'll post it there.

http://www.mathisfunforum.com/viewtopic.php?id=17236

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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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: line

Hi Bob;

Couldn't this be interpreted as meaning that you have a line cutting the triangle into two shapes and the perimeter of each shape being 12?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: line

hi bobbym,

Yes it could.  I feel as if that makes it a lot more difficult.

a line L bisects the area and the perimeter of the triangle AOB.

I took this to mean that the perimeter (24 units) is bisected.

Your two shapes will have perimeters of more than 12 surely?

Hang on! The line forms the border for each shape so its length can be disregarded.

That takes you back to what I did originally I think.

Bob

Last edited by Bob (2012-01-10 07:40:37)

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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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: line

Hi Bob;

Your two shapes will have perimeters of more than 12 surely?

That is what I thought too and a clever argument proposed by anonimnystefy seemed to prove that but working through the problem I found 2 solutions! I will not post mine as your interpretation is probably the one juantheron is looking for.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.