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Calculating the Width of a Rectangle
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Skills Application: Calculating the Width of a Rectangle
Step-by-Step: Calculating the Width of a Rectangle
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The Canadian Northwest Coast Aboriginal wooden bent box is an ingenious example of wood working technology that developed over eons of patients and practice. The boxes are constructed from two pieces of cedar; one for the bottom and the other is a single length of plank notched with a hand tool in three meticulously measured places; the notched cuts are steamed then bent at right angles to form four sides. The last corner of the box is either sewn or pegged together resulting in water tight containers used for storage, cooking pots, serving dishes and coffins. These boxes range in size and shape from simple to highly intricate, carved and painted boxes that measure from a few inches to several feet wide.

## Calculating the Width of a Rectangle ## Did You Know? . . . . . . . . .
3. Our Training Worksheets

To find the width of a rectangle given the perimeter and the length, do the following:  1. Divide the perimeter by 2  2. Take away the length (or subtract the length)

EXAMPLE:

The perimeter of a deck is 48 ft. If the length is 16 ft, what is the width?

SOLUTION:

1. Divide the perimeter by 2:

48 divided by 2 = 24

2. Subtract the length from half the perimeter: 24 - 16 = 8

3. State your answer: The width of the deck is 8 ft.

Finding the missing length (L) when perimeter (P) and width (w) are given uses the same 2 steps as finding the width given perimeter and length:

1. Divide the perimeter by 2
2. Take away the width (or subtract the width). It is because length and width are synonyms, so the words can be interchanged in many cases.

EXAMPLE:

The perimeter of a deck is 48 ft. If the width is 8 ft, what is the length?

SOLUTION:

1. Divide the perimeter by 2:

48 divided by 2 = 24

2. Subtract the width from half the perimeter: 24 - 8 = 16

3. State your answer: The length of the deck is 16 ft. ### A Short Review

Why does the Width need calculation? Cant we just measure it? No. It hasnt been built yet. The Perimeter can be fixed or given if we have limited materials or space we cant exceed.

If Perimeter is 50, Length is 20, what do we have left for the Width?

Answer: 50 – 20 – 20 = 10, which must make 2 equal sides, each with a Width of 5. ### Worksheet: Level 1

The operations used are clearly specified. Only one type of mathematical operation is used in a task.

### Worksheet: Level 1 Sample Question

Example: Match the numbers on the right with the corresponding dimensions in the picture and fill in the amounts: ### Worksheet: Level 1 Answer Key  ### Worksheet: Level 2

Tasks involve one or two types of mathematical operation. Few steps of calculation are required.

### Worksheet: Level 2 Sample Question

Example:

Calculate the width or length of the rectangle. Use 2(w + L) = P or any of the 6 rectangle formulas.

w = 4 ft, P = 24 ft

### Worksheet: Level 2 Sample Answer

P = L + w + L + w

Perimeter = length + width + length + width

24 = L + 4 + L + 4

24 − 8 = 2L

16 = 2L

16 ÷ 2 = L

L = 8 ft ### Worksheet: Level 3

Tasks require a combination of operations. Several steps of calculation are required.

### Worksheet: Level 3 Sample Question

Example:

Calculate the width or length of rectangles in the following word problem:

1.  If the perimeter of a sheet of paper is 39 in, its L = 11 in, what is its width?

### Worksheet: Level 3 Sample Answer

1.  P = L + w + L + w

Perimeter = length + width + length + width

39 = 11 + w + 11 + w

39 − 22 = 2w

17 = 2w

17 ÷ 2 = w

w = 8.5 in Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

### Worksheet: Advanced Level Sample Question

Calculate the width of the rectangular bent box given a perimeter of 62 inches and a length of 19 inches.

One way to get the answer, using the formula P = L + w + L + w:
Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look is like this: Calculate the width of the rectangular bent box given a perimeter of 62 inches and a length of 19 inches
.
Another way to get the answer, using the formula P = L + w + L + w:

1.      Identify that the width of the bent box is to be calculated.
2.      Recognize that the length of the board is the perimeter of the bent box.
3.      Recognize that the length of the board yields the width and the length of the finished bent box. In other words, the length of the cedar board yields the perimeter of the whole box. In the calculation below, length numbers (19) relate to the finished box, not the uncut board (62).
4.      Set up the problem:
perimeter – length – length = leftover material for width + width
5.      Calculate: 62  – 19 – 19 = 24
Note: Sessiyám added 19 + 19 = 38, and subtracted just once: 62 – 38 = 24
6.      Take a pencil and write “2 widths = 24” or “2w = 24”
Now this leftover material needs to make 2 pieces of “widths” for the box. Like before, these 2 widths (24) are also coming out of the length of the board. The number 24 could be called length, but it is length of raw material. To avoid changing the point of reference, every number in this problem relates to the finished product.
7.      Set up the problem:
leftover material for width + width ÷ 2 = width
8.      Calculate: 24 ÷ 2 = 12
9.      Take a pencil and write down  “width = 12” or “w = 12”
10.  Write in or sign or inches after the number 12 Now youre done with the math.

The last step: check your work, make sure everything was copied and written correctly then determine that the correct way to write the answer is 12 ft or 12` or 12 inches