A rectangular rug has an area of 21 square feet. Its perimeter is 20 feet. What are the dimensions of the rug? _____ feet by _____ feet

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A rectangular rug has an area of 21 square feet.  Its perimeter is 20 feet. What are the dimensions of the rug?  _____ feet by _____ feet

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Define Rug Area: Let's denote the length of the rug as l feet and the width as w feet. The area of the rug is given by the product of its length and width. Which equation represents the area of a rectangle. Area = l * wCalculate Area: The area of the rectangular rug is given as 21 square feet. Which equation represents the area of this rectangular rug. Substitute 21 for Area in Area = l * w. 21 = l * wDefine Perimeter: The perimeter of a rectangle is given by the sum of twice its length and twice its width. Which equation represents the perimeter of a rectangle. Perimeter = 2l + 2wCalculate Perimeter: The perimeter of the rug is given as 20 feet. Which equation represents the perimeter of this rectangular rug. Substitute 20 for Perimeter in Perimeter = 2l + 2w. 20 = 2l + 2wSolve System of Equations: We now have a system of two equations with two variables: 21 = l * w (1) 20 = 2l + 2w (2) We can solve this system of equations to find the values of l and w.Simplify Perimeter Equation: Let's simplify equation (2) by dividing all terms by 2 to make the calculations easier. 20 / 2 = (2l + 2w) / 2 10 = l + w Now we have a simpler equation: 10 = l + w (3)Express Width in Terms of Length: We can express w from equation (3) in terms of l. w = 10 - l Now we can substitute this expression for w into equation (1).Substitute Width into Area Equation: Substitute w = 10 - l into 21 = l * w. 21 = l * (10 - l) This gives us a quadratic equation: 21 = 10l - l^2Rearrange Quadratic Equation: Rearrange the quadratic equation to standard form. 0 = l^2 - 10l + 21Factor Quadratic Equation: Factor the quadratic equation. (l - 7)(l - 3) = 0Solve for Length: Set each factor equal to zero and solve for l. l - 7 = 0 or l - 3 = 0 This gives us two possible solutions for l: l = 7 or l = 3Find Possible Dimensions: If l = 7, then from equation (3) w = 10 - l, we get w = 10 - 7 = 3. If l = 3, then w = 10 - 3 = 7. So the dimensions of the rug can be either 7 feet by 3 feet or 3 feet by 7 feet.

A rectangular rug has an area of $21 \, \text{square feet}$ . Its perimeter is $20 \, \text{feet}$ . What are the dimensions of the rug? $\newline$ $\_\_\_\_$ feet by $\_\_\_\_$ feet

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A rectangular rug has an area of 21 square feet21 \, \text{square feet}21square feet. Its perimeter is 20 feet20 \, \text{feet}20feet. What are the dimensions of the rug?\newline____\_\_\_\_____ feet by ____\_\_\_\_____ feet

A rectangular rug has an area of $21 \, \text{square feet}$ . Its perimeter is $20 \, \text{feet}$ . What are the dimensions of the rug? $\newline$ $\_\_\_\_$ feet by $\_\_\_\_$ feet