Triangles aren't always triangles, they have a hidden side, an inequality! Whether you're building a ramp or a support the safety of people is a big thing, and triangle inequalities are the hidden suspect. What happens when you know one side, but not the 2 others? Seems like a frightening prospect, but with the concept of Triangle Inequalities you can find the answer in just a moment.
To construct a triangle successfully, the sum of the 2 shorter sides of the triangle must be greater than the largest side of the triangle. It would be impossible to create a triangle if the sum of the 2 shorter sides are less than or equal to the largest side.
The side lengths were 4 units, 8 units, and 2 units. We added 4 and 8 and the sum is 12 which is greater than 2. Then we added 8 and 2 and the sum is 10 which is greater than 4. Next we added 4 and 2 and the sum is 6 which is less than 8. This makes the sides impossible to construct the triangle
The side lengths were 1 unit, 2 units, and 3 units. We added 3 and 1 and the sum is 4 which is greater than 2. Then we added 3 and 2 and the sum is 5 which is greater than 1. Next we added 1 and 2 and the sum is 3 which is equal to 3. This makes the sides impossible to construct the triangle
Here are some problems for you to work on at home:
Tell whether it is possible to construct a triangle with the following side lengths
1.) 3 in, 2.5 in, 5 in 2.) 8 in, 6 in, 5 in
3.) 1.5 in, 2 in, 5 in
Great post! The third problem you gave will not make a triangle. Clear explanation of this math rule, overall.
ReplyDeleteAs you mentioned, the triangle inequality rule can be used for building ramps, safety in constructing buildings, and in jobs like architecture. Here's a website that lists 42 careers that involve the triangle inequality theorem. http://www.xpmath.com/careers/topicsresult.php?subjectID=3&topicID=4
I like how this site also shows what other math skills you need to know for each career. One example, cartographers who are workers who measure the earth. They get to travel in order to create maps, and collect information for others. What are some types of math careers that you might enjoy?