The Formula
Part of the Triangles section of Coddy's Geometry journey. Lesson 10 of 63.
The range rule written once for all triangles: if two sides are a and b, the third side c satisfies
|a - b| < c < a + b
The bars mean the absolute value: the size of the difference, ignoring its sign. That way the order you subtract in does not matter. For sides 3 and 10, |3 - 10| = 7, the same as 10 - 3. So 7 < c < 13.
The rule works for whichever two sides you know, not only the two shortest. It gives the full range at once, both the lowest and the highest length the third side may take.
Challenge
Two sides of a triangle are 5 and 12, and the third side is x. Use the formula to write the range of x on the blank sheet as a chain, then press Check.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingThe Range of the Third SideThe FormulaRecap: The Third Side5The Pythagorean Theorem
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeRecap: The Hypotenuse3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterSides as ExpressionsRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg