Our Solution to the Creating Triangles Problem
What we did: We trialled some side lengths to see which lengths could make a triangle and which sides couldn’t. We used the compasses to make the triangles. We used the compasses to find the point where the sides meet.
What we discovered: We discovered a set of lengths that were able and unable to make triangles. The ones that worked were the two shorter lengths that added up to more than the longest length. The ones that didn’t work we found didn’t have the two smaller lengths add up to the longest side. What we weren't sure about was what if the shorter lengths equalled the longest side. We tested that and found out that they didn’t make the triangles.
Why it is so: IF the two smaller lengths of the triangle add up to the same as the longest side, the two sides intersected only when they met at the line. So it didn’t make a triangle.
THe lengths that didn’t add up to the longest side never intersected so they couldn’t make a triangle.
The lengths that added up to more than the longest side could make a triangle because they were able to intersect at a point that was above the longest side, so made a triangle.
Our Mathematical solution: the two lowest numbers has to be more ( but not equal ) than the length of the longest side. That means that the sum of the two sides can be one nano metre larger ( or more realistically 1 mm longer) to make a very narrow triangle.
A way of writing this as a formula is n2+n3 > n1(longest side)