Scaling and Expanding a Community Garden
A community garden is shown on a rectangular map with dimensions 6 cm by 9 cm. The map scale is 1 cm = 2.5 m. The garden committee plans to expand the actual garden so that each dimension increases by 20%. Before expansion, they need to know the actual area. After expansion, they want to compare the new area to the old area and determine the percent increase in area. The committee also wants to know how many 1.5 m by 2 m raised beds can fit in the expanded garden if the beds must be arranged without overlapping and with no path space considered. Assume the expanded garden remains rectangular and the scale applies only to the original map dimensions.
1. Find the actual dimensions and area of the garden before expansion.
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Using the scale 1 cm = 2.5 m, the actual dimensions are 6 × 2.5 = 15 m and 9 × 2.5 = 22.5 m. The area before expansion is 15 × 22.5 = 337.5 m².
2. Find the dimensions and area after each dimension is increased by 20%, then calculate the percent increase in area.
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Increasing each dimension by 20% multiplies each by 1.2. New dimensions: 15 × 1.2 = 18 m; 22.5 × 1.2 = 27 m. New area = 18 × 27 = 486 m². Percent increase = (486 − 337.5) / 337.5 = 148.5 / 337.5 = 0.44 = 44%. Alternatively, area scales by (1.2)² = 1.44, so the increase is 44%.
3. How many 1.5 m by 2 m raised beds can fit in the expanded garden? Explain your arrangement reasoning.
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The expanded garden is 18 m by 27 m. Each bed is 1.5 m by 2 m. Try orienting beds with the 1.5 m side along the 18 m side: 18 ÷ 1.5 = 12 beds; 27 ÷ 2 = 13.5, so 13 full rows. That gives 12 × 13 = 156 beds. Try the other orientation: 18 ÷ 2 = 9; 27 ÷ 1.5 = 18. That gives 9 × 18 = 162 beds. Since 162 > 156, the maximum number of whole beds is 162, assuming all beds are oriented the same way and no path space is needed.