# Isosceles triangle

1. Jan 6, 2009

### Дьявол

1. The problem statement, all variables and given/known data

Find the sides of isosceles triangle with perimeter 17, if the sides are integers.

2. Relevant equations

N/A

3. The attempt at a solution

The perimeter is equal to 2b+a=17

Now a=17-2b, so b = {1,2,3,4,5,6,7,8} and a= {15,13,11,9,7,5,3,1}

But in my book results the answers are (7,5,5), (5,6,6), (3,7,7), (1,8,8)

What are the rules for isosceles triangle. Must 2b > a ?

Last edited: Jan 6, 2009
2. Jan 6, 2009

### tiny-tim

Hi Дьявол!
You know it must (or the triangle won't "join up")!

3. Jan 6, 2009

### Дьявол

Hello tiny-tim!

I mean 2b>a

I was asking because I wasn't sure

Thanks for the post.

4. Jan 6, 2009

### HallsofIvy

Staff Emeritus
That is often refered to as the "triangle inequality". Since a straight line is the shortest distance between two points, the distance between two vertices going around two sides of the triangle is always greater than the distance going along the one side between them. That is, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

5. Jan 7, 2009

### Дьявол

I understand now.

This works for all sides of the triangle a+b>c.

Thank you HallsofIvy.

Regards.