Are Triangles Possible for any Lengths?

Transcript

Are Triangles Possible for any Lengths?Imagine a small plot of plain land having a tent, a tree, and a pole. Imagine you are at the entrance of the tent and want to go to the tree. Which is the shorter path: (i) the straight-line path to the tree (the red path) or (ii) the straight-line path from the tent to the pole, followed by the straight-line path from the pole to the tree (the yellow path)? Shorter path would be to just go straight. Always. Knowing this, let’s do a triangle question Can this understanding be used to tell something about the existence of a triangle having sidelengths 10 cm, 15 cm and 30 cm? Say we want to go from C to A Let’s try to visualise this Now, Direct path = CA = 30 cm Indirect path = AB + BC = 15 + 10 = 25 cm Let’s try to visualise this Is the direct path length shorter than the roundabout path length? In this case, the direct path is longer, which is absurd. Can such a triangle exist? No. Let’s draw circles and construct this triangle The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Side a 10 Side b 15 Side c (base) A triangle CANNOT be formed! is not greater than 30 This leads us to a theory – Triangle Inequality Theory Let’s learn it