Problem Set Three

First problem solving assignment. Here we go!

1) Question:
An equilateral triangle has a side length of 20. If a square has the same perimeter as the triangle, what's the area of the square?

2) Solution:
Okay, so. First we should get the shapes down.
The triangle is an equilateral. That means that each side is the same length. The square is a square -- four sides, same length for each side.
Now, each side of the triangle is 20 in length (no unit of measurement is given). There are three sides to a triangle. Three multiplied by twenty equals sixty (3*20= 60). The triangle has a perimeter of 60.
The triangle and the square share the same perimeter. That means that each side of the square must be sixty divided by four (60/4), since there are four sides.
Each side of the square, therefore, must be fifteen.
But we aren't just looking for the side length of the square. The question asks for the area.
Area equals length multiplied by width (a=l*w), or in this case, as with all squares, side length multiplied by side length (a=s*s, or a=s^2). In this problem, the area of the square equals fifteen multiplied by fifteen (a=15*15).
In answer to the question, the area of the square is 225.

3) I like this question because it shows the relationship shapes have with each other, and how those relationships can be beneficial to finding the solutions to problems that we may encounter in our work.

4) Through this exercise, I have learned that it's always important to look for relationships within the question, specific data that is relative to two or more distinct parts, that may serve as a basis to find all the needed information.

The end.