How many different isosceles triangles have integer side lengths and perimeter 23?

6 different isosceles triangles.

Step-by-step explanation:

This is a AMC 8 2005 question. (You can search up their solution)

There are 6 triangles:

6, 6, 11

7, 7, 9

8, 8, 7

9, 9, 5

10, 10, 3

11, 11, 1

There are only 6 because if there was an isosceles triangle with side lengths such as 5, 5, 13 the triangle would be impossible since the two smaller side lengths must sum up to be greater than the longest side length.

the answer is 13

step-by-step explanation:

5*5=25

12*12=144

25+144=169

169^2=13

3100

step-by-step explanation: