Solved Exercises on Finding Perimeter of Rectangles in Grade 3

Master finding perimeter of rectangles: calculating perimeters using addition and multiplication, solving rectangle word problems, and comparing rectangular perimeters through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic rectangle perimeter
Exercise 1
Find the perimeter of a rectangle that is 6 units long and 4 units wide.
Definition:

Rectangle perimeter: The total distance around the outside of a rectangle, calculated by adding all four sides

Perimeter calculation methods:
  1. Addition method: Add all four sides (L + W + L + W)
  2. Multiplication method: Use the formula P = 2(L + W)
  3. Double method: P = 2L + 2W
Length
6 units
Width
4 units
Perimeter
2(6+4)=20
Step 1: Identify the dimensions

Length = 6 units, Width = 4 units

Step 2: Apply the perimeter formula

Perimeter = 2 × (Length + Width)

Step 3: Calculate

Perimeter = 2 × (6 + 4) = 2 × 10 = 20 units

6 units
4 units
6 units
4 units
Perimeter = 20 units
Final answer:

The perimeter of the rectangle is 20 units

Applied rules:

• Rectangle perimeter: P = 2(L + W)

• Addition: 6 + 4 = 10

• Multiplication: 2 × 10 = 20

2 Square perimeter
Exercise 2
What is the perimeter of a square with sides of 5 units?
Definition:

Square perimeter: The distance around a square, where all four sides are equal

Side Length
5 units
Number of Sides
4 sides
Perimeter
4 × 5 = 20
Step 1: Identify the side length

All sides of a square are equal: 5 units each

Step 2: Apply the square perimeter formula

Perimeter = 4 × Side length

Step 3: Calculate

Perimeter = 4 × 5 = 20 units

5 units
5 units
5 units
5 units
Perimeter = 20 units
Final answer:

The perimeter of the square is 20 units

Applied rules:

• Square perimeter: P = 4 × Side

• Equal sides: All sides of a square are the same length

• Multiplication: 4 × 5 = 20

3 Missing dimension problem
Exercise 3
A rectangle has a perimeter of 18 units and a width of 3 units. What is its length?
Definition:

Missing dimension: Finding an unknown side length when perimeter and one dimension are known

Perimeter
18 units
Width
3 units
Formula
18 = 2(L+3)
Length
L = 6
Step 1: Write the perimeter formula

P = 2(L + W)

Step 2: Substitute known values

18 = 2(L + 3)

Step 3: Solve for L

18 ÷ 2 = L + 3 → 9 = L + 3 → L = 6

Step 4: Verify the answer

Check: 2(6 + 3) = 2(9) = 18 ✓

6 units
3 units
6 units
3 units
Perimeter = 18 units
Final answer:

The length of the rectangle is 6 units

Applied rules:

• Formula rearrangement: Solve for unknown variable

• Division: To isolate the variable

• Verification: Substitute back to check

Rectangle Perimeter Fundamentals
P = 2(L + W) \text{ or } P = 2L + 2W
Rectangle Perimeter Formula
Rectangle
2(L+W)
Two lengths + two widths
Square
4S
Four equal sides
Addition
L+W+L+W
Sum of all sides
Key definitions:

Perimeter: The distance around the outside of a shape

Rectangle: A four-sided shape with four right angles

Opposite sides: Sides across from each other that are equal in length

Linear units: Units used to measure distance (inches, feet, centimeters, etc.)

3-step perimeter method:
  1. Identify: Find the length and width of the rectangle
  2. Apply: Use the perimeter formula P = 2(L + W)
  3. Calculate: Perform the addition and multiplication
Tip 1: Remember: opposite sides of a rectangle are equal.
Tip 2: Use P = 2(L + W) for efficiency.
Tip 3: Always include units in your final answer.
Tip 4: For squares: P = 4 × side length.
Common errors: Forgetting to multiply by 2, confusing perimeter with area, not including units.
Memory aid: "Perimeter is the fence around the yard - add all sides!"
Key rectangle facts:

• Perimeter = 2 × (Length + Width)

• Opposite sides are equal

• Perimeter is measured in linear units

• Square is a special rectangle

Solution: Exercises 4 to 5
4 Perimeter word problem
Exercise 4
A rectangular garden is 8 feet long and 5 feet wide. If fencing costs $3 per foot, how much will it cost to fence the entire garden?
Definition:

Real-world perimeter problem: A word problem that connects perimeter calculation to practical applications

Garden Dimensions
8 × 5
Perimeter
2(8+5)=26
Cost per Foot
$3
Total Cost
26 × $3 = $78
Step 1: Find the perimeter of the garden

P = 2(L + W) = 2(8 + 5) = 2(13) = 26 feet

Step 2: Calculate the cost

Cost = Perimeter × Price per foot = 26 × $3 = $78

Step 3: Express the final answer

It will cost $78 to fence the garden

8 feet
5 feet
8 feet
5 feet
Perimeter = 26 feet, Cost = $78
Final answer:

It will cost $78 to fence the entire garden

Applied rules:

• Perimeter calculation: P = 2(L + W)

• Multiplication: To find total cost

• Real-world application: Connect math to practical problems

5 Perimeter comparison
Exercise 5
Rectangle A is 4 units by 7 units. Rectangle B is 5 units by 6 units. Which rectangle has the greater perimeter?
Definition:

Perimeter comparison: Calculating and comparing perimeters of different rectangles

Rectangle A
2(4+7)=22
Rectangle B
2(5+6)=22
Comparison
22 = 22
Step 1: Calculate Rectangle A's perimeter

P = 2(4 + 7) = 2(11) = 22 units

Step 2: Calculate Rectangle B's perimeter

P = 2(5 + 6) = 2(11) = 22 units

Step 3: Compare the perimeters

22 = 22, so both perimeters are equal

Step 4: State the conclusion

Both rectangles have the same perimeter

4 units
7 units
4 units
7 units
5 units
6 units
5 units
6 units
Rectangle A: 22 units | Rectangle B: 22 units
Final answer:

Both rectangles have the same perimeter (22 units each)

Applied rules:

• Perimeter formula: P = 2(L + W)

• Comparison: Compare calculated values

• Equal perimeters: Different dimensions can have same perimeter

Complete Rectangle Perimeter Guide
P = 2(L + W)
Essential Perimeter Formula
Key definitions:

Perimeter: The total distance around the outside of a shape

Rectangle: A quadrilateral with four right angles and opposite sides equal

Dimension: The measurements of length and width

Linear unit: Unit of measurement for distance (inches, feet, centimeters, etc.)

Advanced perimeter techniques:
  1. Standard formula: P = 2(L + W)
  2. Expanded formula: P = L + W + L + W
  3. Special case (square): P = 4S
  4. Missing dimension: Use algebra to find unknown side
Tip 1: Draw a diagram to visualize the rectangle and its dimensions.
Tip 2: Always check that you've included all four sides.
Tip 3: Practice with physical objects like picture frames or tabletops.
Tip 4: Remember: perimeter measures the outside boundary, not the inside space.
Common errors: Forgetting to multiply by 2, confusing with area, misidentifying dimensions.
Success strategies: Regular practice, visual aids, real-world applications.
Essential perimeter facts:

• Perimeter measures the boundary of a shape

• Perimeter is always expressed in linear units

• Rectangle perimeter = 2 × (length + width)

• Square perimeter = 4 × side length

Perimeter Patterns in Rectangles
Rectangle Dimension vs Perimeter Relationship
Exploring how different length and width combinations affect perimeter:
Same area, different perimeters and vice versa

Rectangle Perimeter Examples:

  • 1×12 rectangle: P = 2(1+12) = 26 units
  • 2×6 rectangle: P = 2(2+6) = 16 units
  • 3×4 rectangle: P = 2(3+4) = 14 units
  • Same area (12 sq units), different perimeters!

Questions & Answers

Question: Why do we multiply by 2 in the perimeter formula? Why not just add the length and width once?

Answer: We multiply by 2 because a rectangle has 4 sides with 2 pairs of equal sides:

  • A rectangle has 2 lengths and 2 widths
  • Instead of writing: L + W + L + W
  • We simplify: 2L + 2W = 2(L + W)

Example: A 3×5 rectangle has sides of 3, 5, 3, and 5 units.

Adding all: 3 + 5 + 3 + 5 = 16 units

Using formula: 2(3 + 5) = 2(8) = 16 units

The multiplication just makes it faster!

Question: Can two rectangles have the same perimeter but different areas?

Answer: Yes! Here's an example:

  • Rectangle 1: 2 units by 8 units → Perimeter = 2(2+8) = 20 units → Area = 2×8 = 16 sq units
  • Rectangle 2: 4 units by 6 units → Perimeter = 2(4+6) = 20 units → Area = 4×6 = 24 sq units

Both rectangles have the same perimeter (20 units) but different areas (16 vs 24 square units).

Perimeter and area are different measurements!

Question: What if the rectangle is not drawn to scale? How do I know which side is length and which is width?

Answer: In grade 3, the problem will usually specify the dimensions or provide a labeled diagram:

  • Look for labels: Numbers next to sides indicating measurements
  • Follow instructions: "Length is 5 units and width is 3 units"
  • Don't worry about scale: Trust the numbers given in the problem

The important thing is to identify the two different measurements and apply the formula.

Remember: P = 2(L + W) works no matter which dimension you call length or width!