Intermath | Workshop Support

 Write-up

Title
The 3rd Side

Problem Statement
The lengths of two sides of a triangle are 5 and 11. If the length of the third side is also a whole number, what are the smallest and largest possible perimeters that the triangle can have?

Problem setup

You are given the lengths of two sides of a triangle.  Determine the length of the unknown side and then the perimeters that the triangle can have.

Plans to Solve/Investigate the Problem

Recommend using the Geometer’s Sketchpad to construct the triangle. Keep in mind that the sum of the lengths of two sides of a triangle must be greater that the length of the third side.

Investigation/Exploration of the Problem

Try letting 5 = 1st side

11 = 2nd side

x = 3rd side

5 + 11 > x         16 > x

5 + x > 11          x > 6

11 + x > 5         x > -6 ( will not work, must be a whole number)

6 < x < 16

In the Geometer’s Sketchpad construct two circles.  Let the radii of the circles be eleven units apart.  One line segment will be 5 units in length. Construct three line segments.

Extensions of the Problem

Try using different set of lengths to determine change.  Ex. 12, 19

Author & Contact
llaster@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials