Problem of the Week Day 1: Week of 6/17/13 - 6/21/13

Today begins the annual summer Problem of the Week. For more recent viewers, the problem of the week is a math problem I create that has five individual parts of it, each part containing a different branch of mathematics. Rather than posting the whole thing at once, I think it is more fun to spread it out across a whole week. So, there is a problem on Monday, which will find the value of one or more variables. Then, the Tuesday problem will take the values of those variables, and do more math on them to receive the next set of answers. You will have to substitute the answers in, and then solve the new problem. This will continue through the whole week, until Friday, when you finally solve for x and complete the problem. All of the answers get posted one month later along with the regular Saturday posting to go along with it.

For the last two years, I had an easy problem and a hard problem. Since I didn’t have as much math knowledge then, I have added a medium problem. To decide which problem(s) you want to attempt, just self-assess your current math ability. If your ability would compare to a sixth or seventh grader’s, you should do the easy problem. If you think you could handle Algebra I content, try the medium one. If you are confident in Geometry and Algebra II, then the hard one would be best for you. The June ones will also be slightly easier than the August ones, but it shouldn’t be much of a difference.

Because of the diversity of the different parts of the problem, I decided to assign each day of the week a branch of math. Monday will be Trigonometry (or something with triangles), Tuesday will be Algebra (or something that you need to know before taking algebra), Wednesday will be Number Theory, Thursday will be Geometry, and Friday will be Probability/Game Theory. So, all three of today’s problems will involve a triangle.

Many of the concepts have been discussed on the blog before, considering that I won't give a problem if I don't think the topics are somewhat cool and interesting. If I were to ask a question about logarithms (I will not be doing that, so that is the example I chose), search logarithms in the search bar, and you should find a post that discusses that concepts. Also, the Problem of the Weeks in 2011 explained every concept before giving the problem, so that should be helpful.

Without any more stalling, here are the problems:

Easy:
Look at the triangle below:

Determine the area and perimeter of this triangle. Use a for the area and p for the perimeter. Do not round answers.

a = ____
p = ____

Medium:
Look at the triangle below:

After finding the value of h, determine the perimeter of this triangle. Use p for the perimeter. Round to the nearest hundredth.

h = ____
p = ____

Hard:
Look at the triangle below:

First, find the values of s and t. Round them to the nearest whole.

s = ____
t = ____

Next, determine the perimeter of the triangle using the rounded values for s and t. Use p for the perimeter.

p = ____

Remember to save your answers for tomorrow. You will need them!