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masha68 [24]
2 years ago
6

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.​
Mathematics
1 answer:
PolarNik [594]2 years ago
6 0

Answer:

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

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

Step-by-step 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

<u>\longrightarrow</u><u> </u><u>Finding </u><u>the</u><u> </u><u>width</u><u> </u><u>of</u><u> </u><u>a</u><u> </u><u>rectangular</u><u> </u><u>garden</u> :

\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{ \frac{4w}{4}  =  \frac{20}{4}}}

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

\mapsto{ \text{w = 5}}

Width of a rectangular garden = 5 feet

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

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

\longrightarrow <u>Finding</u><u> </u><u>the</u><u> </u><u>area</u><u> </u><u>of</u><u> </u><u>a</u><u> </u><u>rectangular</u><u> </u><u>garden</u><u> </u><u>having</u> <u>length of 11 feet and</u><u> </u><u>width</u><u> </u><u>of</u><u> </u><u>5</u><u> </u><u>feet</u> :

\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}

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