Question

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

Answer 1

This is an AMC question from 2005.

Answer 2

A) 2
B) 4
C) 6
D) 9
E) 11

Answer 3

P = side+side+base
23 = side + side + base
23 = s + s + b
23 = 2s + b

Answer 4

I thought, if it has to be isosceles, and have 23 perimeter, an odd number, the non equal side must be odd.

Answer 5

so x is 1,3,5, so on to 21.

Answer 6

23 = 2s + b can be written as
23 = 2y + x if you like

Answer 7

you cant go all the way to 21

Answer 8

ohh!!! 2 sides sum has to more than other side sum. thanks

Answer 9

right..the sum of any two sides is grater than the third side

Answer 10

triangle inequality

Answer 11

i got 11 triangles before.

Answer 12

so now it is....

Answer 13

6 triangles. am i right?

Answer 14

yes

Answer 15

thanks. so much.