- The lot area is 30 m × 40 m = 1200 m².
- The building can occupy at most 50% of the lot, so maximum building area is 600 m².
- Let x be the uniform width of the lawn on all four sides.
- Then the building’s length is (40 - 2x) and its width is (30 - 2x).
- The building area equation is: (40 - 2x)(30 - 2x) = 600.
- Expand: 1200 - 80x - 60x + 4x² = 600 → 4x² - 140x + 1200 = 600.
- Subtract 600: 4x² - 140x + 600 = 0.
- Divide by 4: x² - 35x + 150 = 0.
- Factor: (x - 5)(x - 30) = 0 → x = 5 or x = 30.
- x = 30 is invalid (would make building dimensions negative).
- So x = 5 m.
- Building length = 40 - 2(5) = 30 m.
- Building width = 30 - 2(5) = 20 m.
- 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 application problems worksheet.
