Question

The length of a rectangular garden is 6 more than its width. If the perimeter is 32 feet, what is the width and the area of the garden.​

Answer 1

`{\fbox{ \sf{Width \: of \: a \: rectangular \: garden \: = 5 \: feet}}}`

`\boxed{ \sf{ \: Area \: of \: a \: rectangular \: garden = 55 {ft}^(2)}}`

Explanation:

`\star` Let the width of a rectangular garden be 'w'

`\star` Length of a rectangular garden = 6 + w

`\star` Perimeter of a rectangular garden = 32 feet

`\longrightarrow` Finding the width of a rectangular garden :

`\boxed{ \sf{ \: Perimeter \: of \: a \: rectangle \: = \: 2(length + width}}`

`\mapsto{ \text{32 = 2(6 + w + w)}}`

`\text{Step \: 1 \: : Collect \: like \: terms}`

Like terms are those which have the same base

`\mapsto{ \text{32 = 2(6 + 2w) }}`

`\text{Step \: 2 \: : Distribute \: 2 \: through \: the \: parentheses}`

`\mapsto{ \text{32 = 12 + 4w}}`

`\text{Step \: 3 \: : Swap \: the \: sides \: of \: the \: equation}`

`\mapsto{ \text{4w + 12 = 32}}`

`\text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}`

`\mapsto{ \text{4w = 32 - 12}}`

`\text{Step \: 5 \: : Subtract \: 12 \: from \: 32}`

`\mapsto{ \sf{4w = 20}}`

`\text{Step \: 6 \: : Divide \: both \: sides \: by \: 4}`

`\mapsto{ \sf{ (4w)/(4) = (20)/(4)}}`

`\text{Step \: 7 \: : Calculate}`

`\mapsto{ \text{w = 5}}`

Width of a rectangular garden = 5 feet

`\longrightarrow` Substituting / Replacing the value of w in 6 + w in order to find the length of a rectangular garden

`\mapsto{ \sf{Length = 6 + w = 6 + 5 = \bold{11 \: feet} }}`

`\longrightarrow` Finding the area of a rectangular garden having length of 11 feet and width of 5 feet :

`\boxed{ \sf{Area \: of \: a \: rectangle = length \:∗ \: width}}`

`\mapsto{ \text{Area \: = \: 11 \: ∗ \: 5}}`

`\mapsto{ \sf{Area \: = 55 \: {ft}^(2) }}`

Area of a rectangular garden = 55 ft²

Hope I helped!

Best regards! :D

~
`\sf{TheAnimeGirl}`