Finding Rectangular Dimensions Given Fixed Areas

Here is an excellent video made by one of your classmates to help you understand how to find whole number side lengths of possible rectangles given a fixed area.  Remember, we use the word 'fixed' here to mean constant or "stays the same."

Fixed Area

By: MJ & VM

Fixed Area is where you find different lengths and width(using whole numbers) of rectangles with a certain area. When solving a problem about finding area, simply find factors of the area. The U turn method could be very helpful when finding factors. YOU WILL HAVE TO FIND ALL POSSIBLE DIMENSIONS! Also, perimeter of the rectangle is required. You must find the length and width before finding the perimeter.  A fixed area with dimensions that is the most square like will have the smallest perimeter. The fixed area with dimensions that is the least square like will have the biggest perimeter. I believe this works just because of the squares and rectangles property’s.  

Here’s how a problem would look like step by step:

Find the all the possibilities of rectangles with a fixed area of 8cm2.

1. First, find each possible length and width by finding  factors of eight using the U turn method.

 U Turn Method  

1 * 8

2 * 4

4 * 2

8 * 1

MAKE SURE YOU ALWAYS USE THE OPPOSITE OF EACH RECTANGLE!!!!!!
(If a rectangle is 1 by 8, its opposite would be 8 by 1)

2. After you found all of the fixed area’s factors and its opposites, copy them into the length and width columns in a chart similar to the one below.

Chart

Length	Width	Perimeter	Area
1cm	8cm		8cm2
2cm	4cm		8cm2
4cm	2cm		8cm2
8cm	1cm		8cm2

ALWAYS LABEL YOUR MEASUREMENTS!

3. Once you have the length and width copied into the chart, find the perimeter of each rectangle. The perimeter can be determined by using the formula,2(L+W). Imagining the rectangle could help when finding perimeter.

Length	Width	Perimeter	Area
1cm	8cm	18cm	8cm2
2cm	4cm	12cm	8cm2
4cm	2cm	12cm	8cm2
8cm	1cm	18cm	8cm2

Notice how the perimeter changes. The perimeter of a shape will always stay the same but you can change the area.

Perimeter has to be involved in a fixed area problem because you need both the area and perimeter to describe size. One doesn't give enough information.

STILL REMEMBER TO LABEL PERIMETER AS WELL AS LENGTH, WIDTH, AND AREA!

4. Always check over your work in case you’ve made a mistake.