Using the Properties of Rectangles to Solve Problems
Learning Outcomes
- Use properties of rectangles

What about the area of a rectangle? Remember the rectangular rug from the beginning of this section. It was feet long by feet wide, and its area was square feet. See the image below. Since , we see that the area, , is the length, , times the width, , so the area of a rectangle is . The area of this rectangular rug is square feet, its length times its width.

Properties of Rectangles
- Rectangles have four sides and four right angles.
- The lengths of opposite sides are equal.
- The perimeter, , of a rectangle is the sum of twice the length and twice the width. See the first image.
- The area, , of a rectangle is the length times the width.
Use a Problem Solving Strategy for Geometry Applications
- Read the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.
- Identify what you are looking for.
- Name what you are looking for. Choose a variable to represent that quantity.
- Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
- Solve the equation using good algebra techniques.
- Check the answer in the problem and make sure it makes sense.
- Answer the question with a complete sentence.
example
The length of a rectangle is meters and the width is meters. 1. Find the perimeter 2. Find the area Solution1. | |
Step 1. Read the problem. Draw the figure and label it with the given information. | ![]() |
Step 2. Identify what you are looking for. | the perimeter of a rectangle |
Step 3. Name. Choose a variable to represent it. | Let = the perimeter |
Step 4. Translate. Write the appropriate formula. Substitute. | ![]() |
Step 5. Solve the equation. | |
Step 6. Check: | |
Step 7. Answer the question. | The perimeter of the rectangle is meters. |
2. | |
Step 1. Read the problem. Draw the figure and label it with the given information. | ![]() |
Step 2. Identify what you are looking for. | the area of a rectangle |
Step 3. Name. Choose a variable to represent it. | Let A = the area |
Step 4. Translate. Write the appropriate formula. Substitute. | ![]() |
Step 5. Solve the equation. | |
Step 6. Check: | |
Step 7. Answer the question. | The area of the rectangle is square meters. |
try it
[ohm_question]146510[/ohm_question]example
Find the length of a rectangle with perimeter inches and width inches.Answer: Solution
Step 1. Read the problem. Draw the figure and label it with the given information. | ![]() |
Step 2. Identify what you are looking for. | the length of the rectangle |
Step 3. Name. Choose a variable to represent it. | Let = the length |
Step 4. Translate. Write the appropriate formula. Substitute. | ![]() |
Step 5. Solve the equation. | |
Step 6. Check: | |
Step 7. Answer the question. | The length is inches. |
try it
[ohm_question]146518[/ohm_question]example
The width of a rectangle is two inches less than the length. The perimeter is inches. Find the length and width.Answer: Solution
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
![]() |
Step 4.Translate. Write the appropriate formula. The formula for the perimeter of a rectangle relates all the information. Substitute in the given information. | ![]() |
Step 5. Solve the equation. | |
Combine like terms. | |
Add to each side. | |
Divide by . | |
The length is inches. | |
Now we need to find the width. | |
The width is . | The width is inches. |
Step 6. Check: Since , this works! | |
Step 7. Answer the question. | The length is feet and the width is feet. |
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[ohm_question]146504[/ohm_question]example
The length of a rectangle is four centimeters more than twice the width. The perimeter is centimeters. Find the length and width.Answer: Solution
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.
= length
![]() |
Step 4.Translate. Write the appropriate formula and substitute in the given information. | ![]() |
Step 5. Solve the equation. | (width) length The length is cm. |
Step 6. Check: | |
Step 7. Answer the question. | The length is cm and the width is cm. |
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[ohm_question]146521[/ohm_question] [ohm_question]146522[/ohm_question]example
The area of a rectangular room is square feet. The length is feet. What is the width?Answer: Solution
Step 1. Read the problem. | ![]() |
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. | |
Step 5. Solve the equation. | |
Step 6. Check: | |
Step 7. Answer the question. | The width of the room is feet. |
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[ohm_question]146523[/ohm_question]example
The perimeter of a rectangular swimming pool is feet. The length is feet more than the width. Find the length and width.Answer: Solution
Step 1. Read the problem. Draw the figure and label it with the given information. | ![]() |
Step 2. Identify what you are looking for. | the length and width of the pool |
Step 3. Name. Choose a variable to represent it. The length is feet more than the width. | Let |
Step 4.Translate. Write the appropriate formula and substitute. | ![]() |
Step 5. Solve the equation. | the width of the pool. the length of the pool. |
Step 6. Check: | |
Step 7. Answer the question. | The length of the pool is feet and the width is feet. |
try it
[ohm_question]146524[/ohm_question]Contribute!
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