How mant isosceles triangles, with side lengths that are whole numbers of cm, have a perimeter of 20 cm?

Question

I know the answer is 4, but how did you get the answer??

Answer 1

this is just a guess okay, try drawing it so you can verify

4

9 cm, 9 cm, 2 cm

8 , 8, 4

7, 7, 6

and 6, 6 , 8

Answer 2

I'll help you get started as there are not too many so you should be able to find the rest.

An isosceles triangle has at least two equal sides.

If ABC is an isosceles triangle with base AB and equal sides AC and BC and a perimeter of 20cm then the two equal sides will only be equal whole numbers when the base is an even number such as 2, 4, 6, etc. up to 18.

If AB was an odd number such as 5, then 20-5=15 would the sum of the two equal sides so each one would be 7 1/2 which is not a whole number.

Start with the smallest even number 2 for base AB. Then this leaves 20-2=18 for the sum of the two equal sides. So each of the equal sides is 18/2 = 9. So our first isosceles triangle has base 2 and equal sides 9 giving a perimeter of 2+9+9=20.

There is your first one. It should only take you a minute or two to find the others.

Answer 3

What this wants to know is how many ways can you add two identical whole numbers plus another number to total 20, as isoceles triangles have two equal sides. So you can go from 1, 1, 18 through to 7, 7, 6. There may an equation for this, but I don't know it.

Answer 4

1) 1,1,18
2) 2,2,16
3) 3,3,14
4) 4,4,12
5) 5,5,10
6) 6,6,8
7) 7,7,6
8) 8,8,4
9) 9,9,2

Counted to be 9, but sum of two sides in a triangle MUST be more than the third side. Then #1 - #5 not included. So, the answer is 4.

Answer 5

You can't have something like 1,1,18 because the two shorter sides must add up to more than the third side. So you need to start with 6,6,8 since 5,5,10 and down won't work for the above reason.

6,6,8
7,7,6
8,8,4
9,9,2