1a. Perimeter expressions:
- Rectangle: 2(3a) + 2(2a) = 6a + 4a = 10a
- Triangle: 5b + 5b + (2a + 1) = 10b + 2a + 1
- Parallelogram: 2(2c + 1) + 2(3c - 5) = 4c + 2 + 6c - 10 = 10c - 8
- Pentagon: 3.5e + (2d - 1) + (2e + 1) + (d + 7) + (e + 1) + (3e - 3) = (3.5e + 2e + e + 3e) + (2d + d) + (-1 + 1 + 7 + 1 - 3) = 9.5e + 3d + 5
- Right triangle: (4d + 3) + (7d - 6) + (8d + 1) = 19d - 2
1b. Substituting values a=4, b=2.5, c=8, d=7, e=3:
- Rectangle: 10a = 10 × 4 = 40
- Triangle: 10b + 2a + 1 = 10×2.5 + 2×4 + 1 = 25 + 8 + 1 = 34
- Parallelogram: 10c - 8 = 10×8 - 8 = 80 - 8 = 72
- Pentagon: 9.5e + 3d + 5 = 9.5×3 + 3×7 + 5 = 28.5 + 21 + 5 = 54.5
- Right triangle: 19d - 2 = 19×7 - 2 = 133 - 2 = 131
Extension:
Rectangle area: 5 × 4x = 20x
Triangle area: (1/2) × 10 × (3x + 6) = 5 × (3x + 6) = 15x + 30
Set areas equal: 20x = 15x + 30
Solve: 5x = 30 → x = 6
Parent Tip: Review the logic above to help your child master the concept of algebra substitution worksheet.
