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The length of a rectangle is feet and the width is feet. Find ⓐ the perimeter and ⓑ the area.
Find the length of a rectangle with perimeter inches and width inches.
| Step 1. Read the problem. Draw the figure and label it with the given information. |
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| Step 2. Identify what you are looking for. | the length of the rectangle |
| Step 3. Name. Choose a variable to represent it. | Let L = the length |
| Step 4.
Translate.
Write the appropriate formula. Substitute. |
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| Step 5. Solve the equation. |
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Step 6.
Check:
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| Step 7. Answer the question. | The length is 15 inches. |
Find the length of a rectangle with a perimeter of inches and width of inches.
15 in.
Find the length of a rectangle with a perimeter of yards and width of yards.
9 yd
In the next example, the width is defined in terms of the length. We’ll wait to draw the figure until we write an expression for the width so that we can label one side with that expression.
The width of a rectangle is two inches less than the length. The perimeter is inches. Find the length and width.
| Step 1. Read the problem. | |
| Step 2. Identify what you are looking for. | the length and width of the rectangle |
| Step 3.
Name. Choose a variable to represent it.
Now we can draw a figure using these expressions for the length and width. |
Since the width is defined in terms of the length, we let
L = length. The width is two feet less that the length, so we let
L − 2 = width
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| Step 4.
Translate.
Write the appropriate formula. The formula for the perimeter of a rectangle relates all the information. Substitute in the given information. |
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| Step 5. Solve the equation. | |
| Combine like terms. | |
| Add 4 to each side. | |
| Divide by 4. | |
| The length is 14 inches. | |
| Now we need to find the width. | |
| The width is L − 2. |
The width is 12 inches. |
| Step 6.
Check:
Since , this works! |
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| Step 7. Answer the question. | The length is 14 feet and the width is 12 feet. |
The width of a rectangle is seven meters less than the length. The perimeter is meters. Find the length and width.
18 m, 11 m
The length of a rectangle is eight feet more than the width. The perimeter is feet. Find the length and width.
11 ft , 19 ft
The length of a rectangle is four centimeters more than twice the width. The perimeter is centimeters. Find the length and width.
| Step 1. Read the problem. | |
| Step 2. Identify what you are looking for. | the length and width |
| Step 3. Name. Choose a variable to represent it. | let
W = width
The length is four more than twice the width. 2 w + 4 = length  |
| Step 4.
Translate.
Write the appropriate formula and substitute in the given information. |
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| Step 5. Solve the equation. |
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Step 6.
Check:
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| Step 7. Answer the question. | The length is 12 cm and the width is 4 cm. |
The length of a rectangle is eight more than twice the width. The perimeter is feet. Find the length and width.
8 ft, 24 ft
The width of a rectangle is six less than twice the length. The perimeter is centimeters. Find the length and width.
5 cm, 4 cm
The area of a rectangular room is square feet. The length is feet. What is the width?
| Step 1. Read the problem. |
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| Step 2. Identify what you are looking for. | the width of a rectangular room |
| Step 3. Name. Choose a variable to represent it. | Let W = width |
| Step 4.
Translate.
Write the appropriate formula and substitute in the given information. |
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| Step 5. Solve the equation. |
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Step 6.
Check:
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| Step 7. Answer the question. | The width of the room is 12 feet. |
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