Answer:
10 triangles
Step-by-step explanation:
Let’s consider three scenarios: an equilateral triangle, isosceles and scalene.
1. There are three possibilities for equilateral triangle: 13, 13, 13 17,17,17 23, 23, 23
2. There are 6 possibilities for a isosceles triangle:
There are three choices for the base and for the remaining two sides there are two choice, so 3 x 2 = 6
3. There is only one possibility for a scalene triangle:
Let’s use the triangle theorems to check:
Let the sides be 23,17 and 13. Since every other scalene triangle will have the same sides the SSS (Side-Side-Side) theorem states that any triangle with the same three sides is the same triangle (congruent).
Therefore when adding the three scenarios we will get 3 + 6 + 1 = 10 triangles that can be made.
