Mr. Hodges wants to build a fence around his entire rectangular garden. What is the total distance around the garden? 30 feet Units of Length 1 foot = 12 inches 1 yard = 3 feet 6 yards 1 mile = 5,280 feet 1 kilometer = 1,000 mete 1 meter = 100 centimeter 1 meter = 1,000 millimete 1 centimeter = 10 millimet
The Correct Answer and Explanation is:
To find the total distance around Mr. Hodges’ rectangular garden (also known as the perimeter), we need to ensure all measurements are in the same unit, then use the perimeter formula for a rectangle:
Perimeter (P) = 2 × (length + width)
From the image:
- Length = 30 feet
- Width = 6 yards
We need to convert the width from yards to feet. Using the conversion from the chart:
1 yard = 3 feet
So:
6 yards × 3 feet/yard = 18 feet
Now we have:
- Length = 30 feet
- Width = 18 feet
Now apply the perimeter formula:P=2×(30+18)=2×48=96 feetP = 2 × (30 + 18) = 2 × 48 = \boxed{96 \text{ feet}}P=2×(30+18)=2×48=96 feet
Explanation
This question involves calculating the perimeter of a rectangular garden, which is the total distance around its four sides. To solve it correctly, we first need to ensure all measurements are in the same unit.
In the diagram, the garden’s length is given as 30 feet, and the width is given as 6 yards. Since we can’t directly add feet and yards, we use the conversion chart provided:
1 yard = 3 feet.
So we convert 6 yards into feet:
6 × 3 = 18 feet.
Now both dimensions are in feet:
- Length = 30 feet
- Width = 18 feet
For any rectangle, the perimeter is found using the formula:Perimeter=2×(Length+Width)\text{Perimeter} = 2 × (\text{Length} + \text{Width})Perimeter=2×(Length+Width)
This formula works because a rectangle has two equal lengths and two equal widths, so we add the length and width together, then multiply by 2.
Substituting in the values:2×(30+18)=2×48=96 feet2 × (30 + 18) = 2 × 48 = 96 \text{ feet}2×(30+18)=2×48=96 feet
Therefore, Mr. Hodges needs 96 feet of fencing to go all the way around his rectangular garden. This type of problem helps reinforce the importance of unit conversion, geometry, and attention to detail—critical skills in both academic math and real-world tasks like construction or landscaping.
