1. The lot area is 30 m × 40 m = 1200 m². The building can occupy at most 50% of this, so maximum building area = 600 m².
2. Let x be the uniform width of the lawn on all four sides.
3. The building’s length is (40 - 2x) and its width is (30 - 2x).
4. Set up the equation: (40 - 2x)(30 - 2x) = 600.
5. Expand: 1200 - 80x - 60x + 4x² = 600 → 4x² - 140x + 1200 = 600.
6. Simplify: 4x² - 140x + 600 = 0 → divide by 4: x² - 35x + 150 = 0.
7. Factor: (x - 5)(x - 30) = 0 → solutions x = 5 or x = 30.
8. x = 30 is invalid because it would make building dimensions negative (30 - 2×30 = -30). So x = 5.
9. Building length = 40 - 2(5) = 30 m; building width = 30 - 2(5) = 20 m.
10. Dimensions of the largest building are 30 m by 20 m.
Parent Tip: Review the logic above to help your child master the concept of quadratic word problems worksheet.
