Answer:
[tex] \boxed{\sf Perimeter \: of \: rectangular \: garden = 10x + 2} [/tex]
[tex] \boxed{\sf Area \: of \: rectangular \: garden = 6x^2 + x - 2} [/tex]
Given:
Length of rectangular garden = 2x - 1
Width of rectangular garden = 3x + 2
Step-by-step explanation:
[tex] \sf Perimeter \: of \: rectangular \: garden = 2(Length + Width)[/tex]
[tex] \sf = 2((2x - 1) + (3x + 2))[/tex]
Grouping like terms:
[tex] \sf = 2((2x + 3x) + (2 - 1))[/tex]
2x + 3x = 5x:
[tex] \sf = 2(5x + (2 - 1))[/tex]
2 - 1 = 1:
[tex] \sf = 2(5x + 1)[/tex]
[tex] \sf = (2 \times 5x) + (2 \times 1)[/tex]
2 × 5x = 10x:
[tex] \sf = 10x + (2 \times 1)[/tex]
2 × 1 = 2:
[tex] \sf = 10x + 2[/tex]
[tex] \therefore[/tex]
Perimeter of rectangular garden = 10x + 2
[tex] \sf Area \: of \: rectangular \: garden = Length \times Width[/tex]
[tex] \sf = (2x - 1)(3x + 2)[/tex]
[tex] \sf = 2x(3x + 2) - 1(3x + 2)[/tex]
[tex] \sf = (2x \times 3x) + (2x \times 2) - (1 + 3x) - (1 \times 2)[/tex]
2x × 3x = 6x²:
[tex] \sf = 6 {x}^{2} + (2x \times 2) - (1 + 3x) - (1 \times 2)[/tex]
2x × 2 = 4x:
[tex] \sf = 6 {x}^{2} + 4x - (1 + 3x) - (1 \times 2)[/tex]
1 × 3x = 3x:
[tex] \sf = 6 {x}^{2} + 4x - 3x - (1 \times 2)[/tex]
1 × 2 = 2:
[tex] \sf = 6 {x}^{2} + (4x - 3x) - 2[/tex]
4x - 3x = x:
[tex] \sf = 6 {x}^{2} + x - 2[/tex]
[tex] \therefore[/tex]
Area of rectangular garden = 6x² + x - 2
