All the three sides of triangle ABC have lengths in integral units, with AB = ...

[mtpnd98]

All the three sides of triangle ABC have lengths in integral units, with AB=2001 units and BC=1002 units. The possible number of triangles with this condition is:

 

[Ishuda]

All the three sides of triangle ABC have lengths in integral units, with AB=2001 units and BC=1002 units. The possible number of triangles with this condition is:

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

 

[stapel]

All the three sides of triangle ABC have lengths in integral units, with AB=2001 units and BC=1002 units. The possible number of triangles with this condition is:

What is the least possible (integral) value of the third side? What is the greatest possible (integral) value of the third side? Then how many possible triangles are there?

 

[Mrspi]

All the three sides of triangle ABC have lengths in integral units, with AB=2001 units and BC=1002 units. The possible number of triangles with this condition is:

Here's a hint.

The Triangle Inequality Theorem (as it is called in most textbooks) says:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So, if we have a triangle ABC, with sides of lengths a, b, and c, it must be true that

a + b > c
b + c > a
c + a > b

See if this helps......

 

[mtpnd98]

Here's a hint.

The Triangle Inequality Theorem (as it is called in most textbooks) says:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So, if we have a triangle ABC, with sides of lengths a, b, and c, it must be true that

a + b > c
b + c > a
c + a > b

See if this helps......

Thanks for the reply.

I was also thinking the same thing and by which i concluded that the third side should be < 2001+1002, so there can be 3002 different triangles, but the options are 2001, 2002, 2003, and 2004 respectively.

Please help.

Regards.

 

[mtpnd98]

What is the least possible (integral) value of the third side? What is the greatest possible (integral) value of the third side? Then how many possible triangles are there?

Thanks for the reply.

I was also thinking the same thing and by which i concluded that the third side should be < 2001+1002, so there can be 3002 different triangles, but the options are 2001, 2002, 2003, and 2004 respectively.

Please help.

Regards.

 

[stapel]

What is the least possible (integral) value of the third side? What is the greatest possible (integral) value of the third side? Then how many possible triangles are there?

I was also thinking the same thing and by which i concluded that the third side should be < 2001+1002, so there can be 3002 different triangles, but the options are 2001, 2002, 2003, and 2004 respectively.

Okay; you've answered the "greatest possible" part of what I'd asked. Now, what is your answer to the "least possible" part? For instance, if the third side were one unit long, what kind of triangle would you get? :wink:

 

[mtpnd98]

Okay; you've answered the "greatest possible" part of what I'd asked. Now, what is your answer to the "least possible" part? For instance, if the third side were one unit long, what kind of triangle would you get? :wink:

Oh!!! I got my mistake, the least side will be of 1000 units and so the number of triangles will be 2002 with these conditions.