Solved Exercises on Finding Perimeter Word Problems in Grade 3

Master solving perimeter word problems through real-life applications: gardens, rooms, playgrounds, and more through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Garden fencing
Exercise 1
Sarah wants to put a fence around her rectangular garden. The garden is 10 feet long and 6 feet wide. How many feet of fencing does she need?
Definition:

Word Problem: A math problem presented in a real-world context

Fencing: Material needed to surround the garden, which equals the perimeter

Perimeter: The total distance around the rectangle

Problem-solving method:
  1. Read the problem carefully and identify what is being asked
  2. Find the relevant information (dimensions)
  3. Determine which geometric concept applies (perimeter)
  4. Apply the appropriate formula: P = 2(length + width)
Given
Length = 10 ft, Width = 6 ft
Formula
P = 2(l+w)
Result
P = 32 ft
Step 1: Understand the problem

Sarah needs to fence around her rectangular garden

This means we need to find the perimeter of the rectangle

Step 2: Identify the dimensions

Garden length = 10 feet

Garden width = 6 feet

Step 3: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (10 + 6)

Step 4: Calculate the result

Perimeter = 2 × 16 = 32 feet

Step 5: Answer in context

Sarah needs 32 feet of fencing

Sarah needs 32 feet of fencing
Final answer:

Sarah needs 32 feet of fencing to surround her garden

Applied rules:

• Real-world modeling: Perimeter represents the distance around a shape

• Rectangle Property: Opposite sides are equal

• Perimeter Formula: P = 2(l+w) for rectangles

2 Room border
Exercise 2
Emma wants to put a border around her rectangular bedroom. Her room is 12 feet long and 8 feet wide. How many feet of border does she need?
Definition:

Border: Trim or decoration placed around the edges of a room

Room dimensions: Length and width determine the perimeter

Given
Length = 12 ft, Width = 8 ft
Formula
P = 2(l+w)
Result
P = 40 ft
Step 1: Understand what's needed

Emma wants to put a border around her rectangular bedroom

The border goes around the edges, so we need the perimeter

Step 2: Identify the dimensions

Room length = 12 feet

Room width = 8 feet

Step 3: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (12 + 8)

Step 4: Calculate the result

Perimeter = 2 × 20 = 40 feet

Step 5: State the answer in context

Emma needs 40 feet of border

Emma needs 40 feet of border
Final answer:

Emma needs 40 feet of border to go around her bedroom

Applied rules:

• Perimeter application: Border goes around the edges of the room

• Rectangle perimeter: P = 2(l+w)

• Unit consistency: Answer includes the same units as given

3 Playground border
Exercise 3
The school playground is rectangular and measures 30 yards long and 20 yards wide. The city wants to install a safety border around the entire playground. How many yards of border material are needed?
Definition:

Safety border: Protective barrier around the perimeter of an area

Yards: Unit of measurement (1 yard = 3 feet)

Given
Length = 30 yd, Width = 20 yd
Formula
P = 2(l+w)
Result
P = 100 yd
Step 1: Understand the situation

The city wants to install a safety border around the entire playground

This requires calculating the perimeter of the rectangular playground

Step 2: Identify the dimensions

Playground length = 30 yards

Playground width = 20 yards

Step 3: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (30 + 20)

Step 4: Calculate the result

Perimeter = 2 × 50 = 100 yards

Step 5: Provide the answer in context

The city needs 100 yards of border material

The city needs 100 yards of border material
Final answer:

The city needs 100 yards of border material to surround the playground

Applied rules:

• Real-world application: Safety borders require perimeter measurement

• Perimeter calculation: P = 2(l+w)

• Unit preservation: Answer uses the same units as given (yards)

Rules and methods, laws,...
\(P = 2(l + w)\)
Perimeter of Rectangle
Rectangle
\(4 \text{ sides}, \text{opposite equal}\)
Properties
Perimeter
\(P = 2(l + w)\)
Rectangle formula
Word Problems
\(\text{Context + Math}\)
Real-world application
Key definitions:

Word Problem: A mathematical problem presented in a real-world context that requires translating words into mathematical operations.

Perimeter: The total distance around the outside of a two-dimensional shape.

Rectangle: A four-sided shape with opposite sides equal and all angles 90°.

Context: The real-world situation described in the word problem.

Complete methodology:
  1. Read carefully: Understand the entire problem
  2. Identify key information: Find the numbers and what they represent
  3. Determine what's asked: Understand what you need to find
  4. Translate to math: Convert the words into mathematical terms
  5. Apply formula: Use the appropriate geometric formula
  6. Calculate: Perform the mathematical operations
  7. Answer in context: State the answer in terms of the original problem
Tip 1: Look for keywords like "around," "border," "fence," or "surround" - these often indicate perimeter problems.
Tip 2: Draw a picture of the situation to visualize the problem.
Tip 3: Always include units in your final answer.
Tip 4: Check if your answer makes sense in the real-world context.
Common errors: Misreading the problem, using wrong formula, forgetting to include units, miscalculating.
Memory aids: "Perimeter is the fence around the yard" and "add up all the sides".
Formulas to know by heart:

• Perimeter of rectangle: P = 2(l + w)

• Perimeter of square: P = 4s

• Area of rectangle: A = l × w

• Area of square: A = s²

Solution: Exercises 4 to 5
4 Pool deck problem
Exercise 4
A rectangular swimming pool is 25 feet long and 15 feet wide. The owner wants to build a wooden deck around the entire pool. How many feet of decking material are needed for the border of the pool?
Definition:

Decking material: Wood or composite material used for building decks

Pool border: The edge area surrounding the swimming pool

Given
Length = 25 ft, Width = 15 ft
Formula
P = 2(l+w)
Result
P = 80 ft
Step 1: Understand the requirement

The owner wants to build a deck around the entire pool

This means we need to find the perimeter of the rectangular pool

Step 2: Identify the dimensions

Pool length = 25 feet

Pool width = 15 feet

Step 3: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (25 + 15)

Step 4: Calculate the result

Perimeter = 2 × 40 = 80 feet

Step 5: Answer in the context of the problem

The owner needs 80 feet of decking material for the border

80 feet of decking material needed
Final answer:

The owner needs 80 feet of decking material to build the border around the pool

Applied rules:

• Real-world modeling: Decking material needed equals the perimeter

• Perimeter calculation: P = 2(l+w)

• Practical application: Construction materials based on perimeter measurement

5 Classroom bulletin board
Exercise 5
Ms. Johnson's classroom bulletin board is rectangular. It is 8 feet wide and 4 feet tall. She wants to put a colorful border around the entire bulletin board. How many feet of border does she need?
Definition:

Bulletin board: A board used for posting notices and announcements

Classroom border: Decorative trim around the edge of the board

Given
Width = 8 ft, Height = 4 ft
Formula
P = 2(w+h)
Result
P = 24 ft
Step 1: Identify what's being asked

Ms. Johnson wants to put a border around the entire bulletin board

This means we need to find the perimeter of the rectangular board

Step 2: Identify the dimensions

Bulletin board width = 8 feet

Bulletin board height = 4 feet

(Note: Height here serves as the length of the rectangle)

Step 3: Apply the perimeter formula

Perimeter = 2 × (width + height)

Perimeter = 2 × (8 + 4)

Step 4: Calculate the result

Perimeter = 2 × 12 = 24 feet

Step 5: Provide the answer in context

Ms. Johnson needs 24 feet of border for the bulletin board

Ms. Johnson needs 24 feet of border
Final answer:

Ms. Johnson needs 24 feet of border to go around the bulletin board

Applied rules:

• Context interpretation: Understanding that height is the vertical dimension

• Perimeter application: Border goes around the entire edge

• Dimension recognition: Width and height define the rectangle

Complete Guide: Laws, Methods, Rules, Definitions, Expressions
\(P = 2(l + w)\)
Perimeter of Rectangle
Key definitions:

Word Problem: A mathematical problem presented in a real-world scenario that requires translation of verbal information into mathematical expressions and operations.

Perimeter: The total distance around the boundary of a two-dimensional shape, measured in linear units (inches, feet, yards, centimeters, etc.).

Rectangle: A quadrilateral with four right angles (90°) and opposite sides that are equal in length.

Keywords: Words that indicate specific mathematical operations or concepts (e.g., "around" suggests perimeter, "total" might suggest addition).

Context: The real-world situation that gives meaning to the mathematical problem.

Complete methodology:
  1. Read the entire problem: Get a general understanding of the situation
  2. Identify what is being asked: Determine the specific question
  3. Highlight key information: Circle or note important numbers and facts
  4. Identify the geometric shape: Determine if it's a rectangle, square, etc.
  5. Recognize the concept needed: Perimeter, area, etc.
  6. Write down the formula: Use the appropriate geometric formula
  7. Substitute values: Replace variables with the given measurements
  8. Calculate: Perform the mathematical operations
  9. Check reasonableness: Does the answer make sense in context?
  10. State the answer: Include units and answer in terms of the original problem
Tip 1: Draw a diagram of the situation to visualize the problem and identify dimensions.
Tip 2: Look for clue words: "around," "border," "fence," "edge," "surround," "outline" usually indicate perimeter.
Tip 3: Always double-check that you've included the correct units in your final answer.
Tip 4: Estimate your answer first to check if your calculated result is reasonable.
Rectangle Properties: 4 right angles, opposite sides equal, diagonals equal, sum of angles = 360°.
Perimeter Applications: Fencing, border, trim, frame, edging, railing, outline.
Common Errors: Confusing perimeter with area, misidentifying dimensions, calculation mistakes.
Essential formulas:

• Perimeter of rectangle: P = 2(l + w)

• Perimeter of square: P = 4s

• Area of rectangle: A = l × w

• Area of square: A = s²

• Perimeter of any polygon: Sum of all sides

Perimeter Word Problems Infographic
📏
Key Words for Perimeter

• Around

• Border

• Fence

• Edge

• Surround

• Outline

Perimeter Formula

• Rectangle: P = 2(l + w)

• Square: P = 4s

• Add all sides

• Linear measurement

Problem Steps

• Read carefully

• Find dimensions

• Choose formula

• Calculate

• Include units

Word Problem Workflow
1
Read Problem
2
Find Info
3
Identify Shape
4
Apply Formula
5
Answer Context
Real-World Applications

Gardens, rooms, pools, playgrounds, frames

Anytime you need to go around the edge!

Remember: Perimeter is always about going around the edge!

Questions & Answers

Question: How do I know if a word problem is asking for perimeter or area? They seem similar.

Answer: This is a very common question! Here's how to tell the difference:

  • Perimeter: Questions about going around the edge, fencing, border, trim, or distance around. Keywords: "around," "border," "fence," "edge," "surround."
  • Area: Questions about covering the inside, flooring, painting, or how much space is inside. Keywords: "cover," "floor," "paint," "inside," "space," "surface."

For example: "How much fence do I need?" → Perimeter (going around) "How much carpet do I need?" → Area (covering inside)

Think of perimeter as walking around the outside edge, and area as covering the entire floor.

Question: What should I do if the word problem has extra information that I don't need?

Answer: Many word problems include extra details to test your ability to focus on relevant information. Here's what to do:

  • Read carefully: Don't rush through the problem
  • Identify the question: What exactly are you being asked to find?
  • Highlight important info: Mark the numbers and facts you need
  • Ignore irrelevant details: Skip information that doesn't help solve the problem
  • Double-check: Make sure you have everything needed for your calculation

For example, if a problem says "Sarah's rectangular garden is 10 feet long and 6 feet wide. She planted tomatoes on Monday and carrots on Tuesday. How much fence does she need?" You only need the length and width - the planting days are extra information.

Question: Is it okay to draw pictures when solving word problems? My teacher says to show my work.

Answer: Absolutely! Drawing pictures is not only okay, but it's an excellent strategy for solving word problems. Here's why:

  • Visualization: Pictures help you see the problem clearly
  • Understanding: Drawing forces you to think about what the problem is describing
  • Organization: You can label dimensions on your drawing
  • Checking: You can verify if your answer makes sense with the picture
  • Showing work: Your drawing demonstrates your thinking process

For perimeter problems, drawing a rectangle and labeling the length and width is extremely helpful. Just make sure your drawing represents the situation accurately, and label all important information.