Triangle Inequality (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Triangle Inequality: core idea

Basic inequality.

Can sides $3,4,5$ form a triangle? Type $1$ for yes.

Hint: The sum of two sides must exceed the third. Answer: 1.

1. Can sides $2,3,6$ form a triangle? Type $1$ for yes.
2. Find the greatest integer third side for sides $4$ and $7$ .
3. Find the least integer third side for sides $5$ and $9$ .
4. A triangle has sides $6,8,x$ . If $x$ is an integer, find its greatest value.
5. A triangle has sides $10,3,x$ . Find the least integer $x$ .
6. How many integer values can the third side have if the other sides are $3$ and $5$ ?
7. Can sides $1,1,3$ form a triangle? Type $1$ for yes.
8. Find the perimeter of an equilateral triangle with side $7$ .
9. A triangle has sides $5,5,8$ . Is it isosceles? Type $1$ for yes.