A Description Of The Problem Solving Report Essay

2025 Words Sep 23rd, 2016 9 Pages
A Description of the Problem For the problem-solving report, we have a 4x4 grid that we have to find as many rectangles as we can. The rectangles that can be found on the 4x4 grid ranges from 1x1 rectangles to a 4x4 rectangle. According to MathisFun.com a rectangle is, “a 4-sided flat shape with straight sides where all interior angles are right angles (90°). Also opposite sides are parallel and of equal length. Example: Another factor we have to consider is the lines provided on the 4x4 grid must make up the sides of the rectangles.
Solution to the Problem:
I found there are 100 rectangles in a 4x4 grid.
General Problem:
(n^2 〖(n+1)〗^2)/4
Strategies to Finding the Solution: Once I understood what the question was asking, I tried to figure different methods that would simplify the problem. The first method that I thought of was finding how many rectangles in a 1x1 grid, 2x2 grid, and a 3x3 grid. The first grid that I worked with was the 1x1 grid because it seemed to be the easiest.

When doing the 1x1 grid all I had to do was briefly look at the grid and I knew there was only one rectangle. After figuring out how many rectangles were in a 1x1 grid I moved onto the 2x2 grid. However, this time I could not briefly look at the grid and know how many rectangles there were. This time when counting the squares I decided that I was going to label each square in the 2x2 grid, like the grid below. Now with the entire 2x2 gird labeled I could give each rectangle I found a…

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