Triangle Inequality Theorem Calculator

Your details

Units are cosmetic here - only the ratios matter for the theorem.
Length of the first side.
Length of the second side.
Length of the third side.
Triangle possible?Valid triangle
Yes - valid triangle

Whether the three sides satisfy all three triangle inequalities

a + b > cPASS (5 + 7 = 12.0000 > 9, margin 3.0000)
a + c > bPASS (5 + 9 = 14.0000 > 7, margin 7.0000)
b + c > aPASS (7 + 9 = 16.0000 > 5, margin 11.0000)
Valid range for side c2.0000 < c < 12.0000
Perimeter21
Conditions failed0

These three sides form a valid triangle.

  • All three inequalities hold, so these sides can form a triangle.
  • The shortest side is 5 and the longest is 9.
  • For any two sides of length 5 and 7, side c must lie strictly between 2.000 and 12.000.

Next stepTo go further, use a triangle calculator to find the angles, area, and altitudes from these side lengths.

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