Answer:
[tex]{\fbox{ \sf{Width \: of \: a \: rectangular \: garden \: = 5 \: feet}}}[/tex]
[tex] \boxed{ \sf{ \: Area \: of \: a \: rectangular \: garden = 55 {ft}^{2}}}[/tex]
Step-by-step explanation:
[tex] \star[/tex] Let the width of a rectangular garden be 'w'
[tex] \star[/tex] Length of a rectangular garden = 6 + w
[tex] \star[/tex] Perimeter of a rectangular garden = 32 feet
[tex] \longrightarrow[/tex] Finding the width of a rectangular garden :
[tex] \boxed{ \sf{ \: Perimeter \: of \: a \: rectangle \: = \: 2(length + width}}[/tex]
[tex] \mapsto{ \text{32 = 2(6 + w + w)}}[/tex]
[tex] \text{Step \: 1 \: : Collect \: like \: terms}[/tex]
Like terms are those which have the same base
[tex] \mapsto{ \text{32 = 2(6 + 2w) }}[/tex]
[tex] \text{Step \: 2 \: : Distribute \: 2 \: through \: the \: parentheses}[/tex]
[tex] \mapsto{ \text{32 = 12 + 4w}}[/tex]
[tex] \text{Step \: 3 \: : Swap \: the \: sides \: of \: the \: equation}[/tex]
[tex] \mapsto{ \text{4w + 12 = 32}}[/tex]
[tex] \text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}[/tex]
[tex] \mapsto{ \text{4w = 32 - 12}}[/tex]
[tex] \text{Step \: 5 \: : Subtract \: 12 \: from \: 32}[/tex]
[tex] \mapsto{ \sf{4w = 20}}[/tex]
[tex] \text{Step \: 6 \: : Divide \: both \: sides \: by \: 4}[/tex]
[tex] \mapsto{ \sf{ \frac{4w}{4} = \frac{20}{4}}}[/tex]
[tex] \text{Step \: 7 \: : Calculate}[/tex]
[tex] \mapsto{ \text{w = 5}}[/tex]
Width of a rectangular garden = 5 feet
[tex] \longrightarrow[/tex] Substituting / Replacing the value of w in 6 + w in order to find the length of a rectangular garden
[tex] \mapsto{ \sf{Length = 6 + w = 6 + 5 = \bold{11 \: feet} }}[/tex]
[tex] \longrightarrow[/tex] Finding the area of a rectangular garden having length of 11 feet and width of 5 feet :
[tex] \boxed{ \sf{Area \: of \: a \: rectangle = length \:∗ \: width}}[/tex]
[tex] \mapsto{ \text{Area \: = \: 11 \: ∗ \: 5}}[/tex]
[tex] \mapsto{ \sf{Area \: = 55 \: {ft}^{2} }}[/tex]
Area of a rectangular garden = 55 ft²
Hope I helped!
Best regards! :D
~[tex] \sf{TheAnimeGirl}[/tex]
