The Good, The Bad, The Inequality - Triangle Inequalities

              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

The Plus Side of Percents- Interest Earned

Percent doesn't always have to mean extra money that you have to pay.  When we experience a gain, percentage can be a powerful tool that helps measure our success. Here are some ways percents may work in your favor.

When looking back on your test results from before and after you can find the percent growth.  For instance,  if you had gotten 37 out of 48 questions correct on your first test, and then you went up to get 45 out of 48 points.  What was the percent increase?

Percent increase =  change in amount ÷ original amount.  

                                  45-37  ÷  37

                                      8     ÷  37   = .22  or a 22 % increase.
Check out this neat game using Percent Change, it's called the Rags to Riches Game.  Are you ready to use percents to solve problems and earn the monetary rewards?

Percents can also be used to find out how much interest you can expect  to earn for saving or investing money?   If a person saved $10 a week in "the bank of Dad" for 1 year and each week Dad paid 7% interest on the amount in the account, how much money would they have at the end of the year?

Without interest=   $20 x 52 weeks = $1,040 total 

With interest =  $20 per week X 1.07 per week = $1,111.40 total

Interest earned   1111.40-1040 = $71.40
Make a spreadsheet for your saving goals.  Try changing the amount you save and percent interest earned. 

When spending money percents discounts can be used to find which store offers the best deal. An example may be a new computer that was regularly $700 is now on sale for $550, another store offers a 25% discount and will match the price.  

Regular price $700 - Sale Price $550

Regular price $700 x .75 (percent you pay for the item after 25% off) =  $525

Difference in price $550-$525 = $50
Here's a link from Mathopolis where you can find more information and practice solving percent problems.

What are some experiences you've had with the plus sides of percents?  When the percents are used to tell stories of success, doing the math is fun!