The perimeter of a rectangular dining room is 22 meters. The area is 24 square meters. What are the dimensions of the dining room? _____ meters by _____ meters

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The perimeter of a rectangular dining room is 22 meters.  The area is 24 square meters. What are the dimensions of the dining room?  _____ meters by _____ meters

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Define Variables: Let's denote the length of the dining room as l meters and the width as w meters. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w. Since we know the perimeter is 22 meters, we can write the equation: 22 = 2l + 2wPerimeter Equation: We can simplify the equation by dividing both sides by 2 to find the sum of the length and width: 11 = l + wSimplify Perimeter Equation: The area (A) of a rectangle is given by the formula A = l * w. We know the area is 24 square meters, so we can write the equation: 24 = l * wArea Equation: Now we have a system of two equations with two variables: 1. 11 = l + w 2. 24 = l * w We can solve this system by expressing one variable in terms of the other using the first equation and then substituting it into the second equation. Let's express w in terms of l: w = 11 - lSolve System of Equations: Substitute w from the previous step into the area equation: 24 = l * (11 - l) This gives us a quadratic equation: 24 = 11l - l^2 Rearranging the terms to set the equation to zero: l^2 - 11l + 24 = 0Express Width in Terms of Length: We can factor the quadratic equation: (l - 8)(l - 3) = 0 This gives us two possible solutions for l: l = 8 or l = 3Substitute Width into Area Equation: If l = 8, then substituting back into w = 11 - l gives us: w = 11 - 8 w = 3 And if l = 3, then: w = 11 - 3 w = 8 So the dimensions of the dining room can be either 8 meters by 3 meters or 3 meters by 8 meters since a rectangle's length and width are interchangeable.

The perimeter of a rectangular dining room is $22$ meters. The area is $24$ square meters. What are the dimensions of the dining room? $\newline$ $\_\_\_$ meters by $\_\_\_$ meters

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The perimeter of a rectangular dining room is 222222 meters. The area is 242424 square meters. What are the dimensions of the dining room?\newline___\_\_\____ meters by ___\_\_\____ meters

The perimeter of a rectangular dining room is $22$ meters. The area is $24$ square meters. What are the dimensions of the dining room? $\newline$ $\_\_\_$ meters by $\_\_\_$ meters