A rectangular sticker has an area of 28 square centimeters and a perimeter of 22 centimeters. What are the dimensions of the sticker? _____ centimeters by _____ centimeters

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A rectangular sticker has an area of 28 square centimeters and a perimeter of 22 centimeters. What are the dimensions of the sticker?  _____ centimeters by _____ centimeters

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Define Variables: Let l be the length and w be the width of the rectangle. The area of a rectangle is given by the formula A = l * w.Area and Perimeter Formulas: The area of the sticker is given as 28 square centimeters. Substitute 28 for A in the formula A = l * w. 28 = l * wSubstitute Values: The perimeter of a rectangle is given by the formula P = 2l + 2w. The perimeter of the sticker is given as 22 centimeters. Substitute 22 for P in the formula P = 2l + 2w. 22 = 2l + 2wSimplify Perimeter: Divide the perimeter equation by 2 to simplify. 22 / 2 = (2l + 2w) / 2 11 = l + wSolve System of Equations: We now have a system of two equations with two variables: 28 = l * w (Area equation) 11 = l + w (Perimeter equation) We can solve this system by expressing one variable in terms of the other using the perimeter equation and then substituting into the area equation.Express Width in Terms of Length: Express w in terms of l using the perimeter equation. w = 11 - lSubstitute Width into Area Equation: Substitute w = 11 - l into the area equation 28 = l * w. 28 = l * (11 - l)Expand and Rearrange Equation: Expand the equation and move all terms to one side to form a quadratic equation. 28 = 11l - l^2 0 = l^2 - 11l + 28Factor Quadratic Equation: Factor the quadratic equation. 0 = (l - 4)(l - 7)Solve for Length: Solve for l by setting each factor equal to zero. l - 4 = 0 or l - 7 = 0 l = 4 or l = 7Find Possible Dimensions: If l = 4, then w = 11 - l = 11 - 4 = 7. If l = 7, then w = 11 - l = 11 - 7 = 4. So the dimensions of the sticker can be either 4 cm by 7 cm or 7 cm by 4 cm.

A rectangular sticker has an area of $28\,\text{square centimeters}$ and a perimeter of $22\,\text{centimeters}$ . What are the dimensions of the sticker? $\newline$ $\_\_\_\_$ centimeters by $\_\_\_\_$ centimeters

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A rectangular sticker has an area of 28 square centimeters28\,\text{square centimeters}28square centimeters and a perimeter of 22 centimeters22\,\text{centimeters}22centimeters. What are the dimensions of the sticker?\newline____\_\_\_\_____ centimeters by ____\_\_\_\_____ centimeters

A rectangular sticker has an area of $28\,\text{square centimeters}$ and a perimeter of $22\,\text{centimeters}$ . What are the dimensions of the sticker? $\newline$ $\_\_\_\_$ centimeters by $\_\_\_\_$ centimeters