The Range of the Third Side

Part of the Triangles section of Coddy's Geometry journey. Lesson 9 of 63.

Two sides of a triangle are 9 and 4. How long can the third side x be? It must be shorter than the other two together: x < 9 + 4. And the 9 must not beat 4 and x together, so x must be longer than their difference: x > 9 - 4.

Both at once is the chain 9 - 4 < x < 9 + 4, so 5 < x < 13. Any length strictly between 5 and 13 works. At 5 or 13 the triangle goes flat.

If the sides must be whole numbers, list them: 6, 7, 8, 9, 10, 11 and 12, so seven different triangles. The ends 5 and 13 are left out.

On the board you get a blank sheet and write the range yourself, as a chain like 5 < x < 13. Choosing the two ends is the whole skill: nothing writes them for you.

Challenge

Two sides of a triangle are 11 and 4, and the third side is x. On the blank sheet, write the range of x as a chain (or as two lines, one for each end). Then press Check.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Triangles

2The Triangle Inequality

Can Three Sticks Meet?Exactly ReachingThe Range of the Third SideThe Formula Recap: The Third Side

5The Pythagorean Theorem

Squares on the Sides Finding the Hypotenuse Pythagorean Triples When It Is Not Whole Recap: The Hypotenuse

8Special Right Triangles

The 45-45-90 Triangle Legs from the Hypotenuse The 30-60-90 Triangle All Three Sides Which Triangle Is It?Recap: Special Triangles

11Two Tools at Once

Height of an Isosceles Area from the Height The Equilateral Triangle Right Triangle Perimeter Recap: Two Tools