The image you've uploaded is a
perimeter word problem worksheet with five questions, each involving calculating the perimeter of different shapes. The solutions are already provided in red text, but I'll go through each problem step by step to explain how the answers were derived.
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🔷 Problem 1: Mary's Square Yard
> Mary is going to fence in her back yard. The yard is square in shape and one of the sides measures 12 feet. How many feet of fence should Mary purchase?
Solution:
- A
square has
4 equal sides.
- If one side = 12 feet, then:
$$
\text{Perimeter} = 4 \times 12 = 48 \text{ feet}
$$
Wait! There's a
mistake in the answer shown on the worksheet.
✔ Correct Answer:
$$
4 \times 12 = 48 \text{ feet}
$$
✘ But the worksheet says:
"12 ft × 4 = 36 feet" → This is
incorrect (12 × 4 = 48, not 36).
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🔷 Problem 2: Martha’s Dog Pen (Rectangle)
> Martha needs to put a fence around her dog’s pen. She wants the pen to be a rectangle that is 11 feet long and 5 feet wide. How much fence will she need?
Solution:
- For a
rectangle, perimeter = $ 2 \times (\text{length} + \text{width}) $
- So:
$$
2 \times (11 + 5) = 2 \times 16 = 32 \text{ feet}
$$
Or:
$$
(2 \times 11) + (2 \times 5) = 22 + 10 = 32 \text{ feet}
$$
✔ Answer is correct:
32 feet
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🔷 Problem 3: Arnold’s Picture Frame
> Arnold wants to put a frame around a picture that is 24 inches by 12 inches. How many inches of frame would be required?
Solution:
- Again, this is a rectangle.
- Perimeter = $ 2 \times (\text{length} + \text{width}) $
- $$
2 \times (24 + 12) = 2 \times 36 = 72 \text{ inches}
$$
Or:
$$
(2 \times 24) + (2 \times 12) = 48 + 24 = 72 \text{ inches}
$$
✔ Answer is correct:
72 inches
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🔷 Problem 4: Bernard’s Room
> Bernard wants to measure the perimeter of his room. The room is rectangular in shape and is 11 feet long and 12 feet wide. What is the perimeter of the room?
Solution:
- Perimeter = $ 2 \times (11 + 12) = 2 \times 23 = 46 $ feet
- Or:
$$
(2 \times 11) + (2 \times 12) = 22 + 24 = 46 \text{ feet}
$$
✔ Answer is correct:
46 feet
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🔷 Problem 5: Bonnie’s Triangular Field
> Bonnie’s soccer coach has the team run around a triangular field. If the sides of the triangle are 50 yards, 75 yards, and 115 yards. How far will Bonnie run?
Solution:
- For a
triangle, perimeter = sum of all three sides
- $$
50 + 75 + 115 = 240 \text{ yards}
$$
✔ Answer is correct:
240 yards
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✔ Final Summary:
| Problem | Shape | Given Dimensions | Correct Perimeter |
|--------|-----------|------------------------------|-------------------|
| 1 | Square | Side = 12 ft |
48 ft ✘ (Worksheet says 36 ft — incorrect) |
| 2 | Rectangle | 11 ft × 5 ft |
32 ft ✔ |
| 3 | Rectangle | 24 in × 12 in |
72 in ✔ |
| 4 | Rectangle | 11 ft × 12 ft |
46 ft ✔ |
| 5 | Triangle | 50 yd, 75 yd, 115 yd |
240 yd ✔ |
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🛠️ Key Concepts:
-
Square: Perimeter = $ 4 \times \text{side} $
-
Rectangle: Perimeter = $ 2 \times (\text{length} + \text{width}) $
-
Triangle: Perimeter = sum of all three sides
---
❗Note:
There is a
mistake in
Problem 1. The correct calculation is:
$$
12 \times 4 = 48 \text{ feet}, \text{ not } 36 \text{ feet}.
$$
So,
Mary should buy 48 feet of fence, not 36.
Let me know if you'd like a corrected version of the worksheet!
Parent Tip: Review the logic above to help your child master the concept of perimeter word problems worksheet.
