A rectangular garden has a length of 15 meters and a width that is 3 meters less than the length. If the garden is expanded by increasing both dimensions by 2 meters, what is the new area of the garden? - Coaching Toolbox
Rectangular Garden Expansion: How Increasing Dimensions Boosts Garden Area
Rectangular Garden Expansion: How Increasing Dimensions Boosts Garden Area
A well-planned rectangular garden not only enhances your outdoor space but also contributes to a healthier, more beautiful environment. Take, for example, a rectangular garden with a length of 15 meters and a width 3 meters shorter than its length. If this garden is expanded by increasing both dimensions by 2 meters, what is the new area? Letβs explore the math behind this transformation and why garden expansion matters.
Understanding the Original Garden
Understanding the Context
First, determine the original dimensions:
- Length = 15 meters
- Width = Length β 3 meters = 15 β 3 = 12 meters
The original area is calculated by multiplying length and width:
Area = Length Γ Width = 15 Γ 12 = 180 square meters
Expanding the Garden
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Key Insights
Now, the garden is expanded by increasing both dimensions by 2 meters:
- New Length = 15 + 2 = 17 meters
- New Width = 12 + 2 = 14 meters
Calculating the New Area
To find the new area, multiply the updated length by the updated width:
New Area = 17 Γ 14
To simplify:
17 Γ 14 = (10 + 7) Γ (10 + 4) = 10Γ10 + 10Γ4 + 7Γ10 + 7Γ4 = 100 + 40 + 70 + 28 = 238 square meters
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Why Expand a Garden?
Expanding garden size offers multiple benefits:
- More space for planting vegetables, flowers, or herbs
- Improved aesthetic appeal and natural ambiance
- Greater area for relaxation and outdoor activities
- Better biodiversity by accommodating diverse plant species
Additionally, increasing the garden by even just 2 meters on all sides significantly improves usable spaceβgoing from 180 mΒ² to 238 mΒ², an increase of 58 mΒ².
Conclusion
A rectangular garden with a length of 15 meters and width 12 meters expands to 17 meters by 14 meters when enlarged by 2 meters on each side, resulting in a new total area of 238 square meters. Whether for practical gardening needs or enhancing outdoor living, strategic expansion transforms a modest plot into a more productive and beautiful space.
For anyone planning garden improvements, understanding how dimension changes affect area helps optimize spaceβmaximizing both function and beauty. Start small, think big, and watch your garden grow.
