Question

Johnny’s vegetable garden is rectangular. The length of the garden is 2x-1 and the width of the garden is 3x+2. Find the Perimeter and Area of the garden.

Answer 1

Perimeter = 10x+2 m

Area = 6x²+x-2 m²

Explanation:

Length of garden (l) = 2x-1

width or breadth of garden ( b) = 3x+2

Now,

Perimeter of the garden (p) = 2( l + b)

= 2 ( 2x-1 + 3x+2 )

= 2 ( 5x + 1 )

= 10x+2 m. ( Answer )

Again,

Area of garden (a) = l * b

= ( 2x-1 ) ( 3x+2 )

= 2x ( 3x+2 ) -1 ( 3x+2 )

= 6x² + 4x - 3x - 2

= 6x²+x-2 m². ( Answer )

Answer 2

`\boxed{\sf Perimeter \: of \: rectangular \: garden = 10x + 2}`

`\boxed{\sf Area \: of \: rectangular \: garden = 6x^2 + x - 2}`

Given:

Length of rectangular garden = 2x - 1

Width of rectangular garden = 3x + 2

Explanation:

`\sf Perimeter \: of \: rectangular \: garden = 2(Length + Width)`

`\sf = 2((2x - 1) + (3x + 2))`

Grouping like terms:

`\sf = 2((2x + 3x) + (2 - 1))`

2x + 3x = 5x:

`\sf = 2(5x + (2 - 1))`

2 - 1 = 1:

`\sf = 2(5x + 1)`

`\sf = (2 * 5x) + (2 * 1)`

2 × 5x = 10x:

`\sf = 10x + (2 * 1)`

2 × 1 = 2:

`\sf = 10x + 2`

`\therefore`

Perimeter of rectangular garden = 10x + 2

`\sf Area \: of \: rectangular \: garden = Length * Width`

`\sf = (2x - 1)(3x + 2)`

`\sf = 2x(3x + 2) - 1(3x + 2)`

`\sf = (2x * 3x) + (2x * 2) - (1 + 3x) - (1 * 2)`

2x × 3x = 6x²:

`\sf = 6 {x}^(2) + (2x * 2) - (1 + 3x) - (1 * 2)`

2x × 2 = 4x:

`\sf = 6 {x}^(2) + 4x - (1 + 3x) - (1 * 2)`

1 × 3x = 3x:

`\sf = 6 {x}^(2) + 4x - 3x - (1 * 2)`

1 × 2 = 2:

`\sf = 6 {x}^(2) + (4x - 3x) - 2`

4x - 3x = x:

`\sf = 6 {x}^(2) + x - 2`

`\therefore`

Area of rectangular garden = 6x² + x - 2