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a rectangle has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length, in feet, of the mat.
Then find the area, in square feet, of the mat.

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TheSarcasmic

❍ Concept :-

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We have been provided with some information regarding a rectangular shaped mat. And on the basis of that information, we will create some assumptions and create and equation and equate it to get our required answer.

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✱ Given Information :-

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A rectangular mat with,

  • Perimeter = 36 ft.
  • Length = twice the width

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✱ To Find :-

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  • The dimensions of the mat
  • Area of the mat

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✱ Formula Used :-

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[tex] \diamond \: \underline{ \boxed{\begin{array}{cc} \sf1. \: Perimeter_{Rectangle} = 2(l+b) \\ \\ \sf 2. ~Area_{Rectangle} = l\times b \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}}} \: \star \\ [/tex]

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✱ Solution :-

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Let the breadth of the mat be x, therefore,

  • Length = 2x

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Now, according to the question,

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[tex] \sf \hookrightarrow 36 \: = 2(2x + x) \\ \\ \\ \sf \hookrightarrow 6x = 36 \: ft. \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow x = \cancel\frac{36}{6} = 6 \: ft. \: \: \\ [/tex]

Thus,

  • Length = 2x = 2 x 6 = 12 ft.
  • Breadth = x = 6 ft.

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Now, we have to find out the area of the mat, thus,

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[tex] \sf \hookrightarrow Area=6 \times 12 \\ \\ \\\sf \hookrightarrow Area=72 \: sq. ~ft. \\ \\ [/tex]

Thus, the area of the mat is 72 sq. ft.

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[tex]\underline {\rule{221pt}{2.5pt}} \\ \\ [/tex]

reiramasu

Answer:

72 sq. feet

Step-by-step explanation

Since the perimeter is 36 feet and the length is 2w, you have to do the guess and check method.

I already did the guess and check method. So, here's how it became:

length =12

width=6

because 6x2=12 or 12 divide 2=6.

12 + 6 + 12 + 6.

12+6= 18. 12+6=18. 18+18=36 feet.

To find the area of a rectangle, you have to do L times W.

Which means 12x6.

12x6=72 sq. feet.

I hope this helps!!!

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