Solving Isosceles Triangle with Perimeter 17: Integers as Sides

[Дьявол]

Homework Statement

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

Homework Equations

N/A

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 ?

Thanks in advance.

 

[tiny-tim]

Hi Дьявол!

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

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

Why were you asking?

 

[Дьявол]

Hi Дьявол!


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

Why were you asking?

Hello tiny-tim!

I mean 2b>a

I was asking because I wasn't sure

Thanks for the post.

 

[HallsofIvy]

That is often referred 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.

 

[Дьявол]

That is often referred 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.

I understand now.

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

Thank you HallsofIvy.

Regards.