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Triangle Inequality Checker

Triangles · Class IX

Pick three side lengths a, b, c. Do they form a valid triangle?

3
type a value
0.520
4
type a value
0.520
5
type a value
0.520
Live values
  • a + b > c?1
  • b + c > a?1
  • a + c > b?1
  • Valid triangle?1
Live readout
a + b > c?1
b + c > a?1
a + c > b?1
Valid triangle?1
Side a3
Side b4
Side c5

Formulas in this lab

  • a + b > c?
    a+b>ca + b > c
  • b + c > a?
    b+c>ab + c > a
  • a + c > b?
    a+c>ba + c > b
  • Valid triangle?
    all three?\text{all three?}
Tip: A triangle exists only when each side is strictly less than the sum of the other two.

Frequently asked questions

▶What is the triangle inequality?

For any triangle with sides a, b, c, the sum of any two sides must exceed the third: $a + b > c$, $b + c > a$, and $c + a > b$. If even one inequality fails, the three lengths cannot close into a triangle.

▶How do I use this lab?

Slide the three sides a, b, c between 0.5 and 20. The lab checks all three inequalities and tells you whether a valid triangle is formed. Try 3, 4, 5 (works) versus 1, 2, 5 (fails).

▶Common mistake on this topic

Students check only one inequality and stop. You must verify all three pairs before concluding a triangle is possible. In board exams, write each inequality clearly to score full marks.

▶Where do we use this idea?

Carpenters cutting bamboo poles for a frame check the triangle rule before joining sides. If a tailor cuts three strips for a triangular flag, the longest must be less than the sum of the other two, else the flag won't close.