A rectangular sticker has a perimeter of 26 centimeters. Its area is 36 square centimeters. What are the dimensions of the sticker? _____ centimeters by _____ centimeters

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A rectangular sticker has a perimeter of 26 centimeters.  Its area is 36 square 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 rectangular sticker. The perimeter of a rectangle is given by the formula P = 2l + 2w.Perimeter Equation: Given the perimeter of the sticker is 26 centimeters, we can write the equation 26 = 2l + 2w.Simplify Perimeter: Simplify the perimeter equation by dividing all terms by 2 to get 13 = l + w.Area Formula: The area of a rectangle is given by the formula A = lw. Given the area of the sticker is 36 square centimeters, we can write the equation 36 = lw.System of Equations: We now have a system of two equations: 1. 13 = l + w 2. 36 = lw We will solve this system to find the values of l and w.Express Width: From the first equation, we can express w in terms of l: w = 13 - l.Substitute Width: Substitute w = 13 - l into the second equation 36 = lw to get 36 = l(13 - l).Distribute Equation: Distribute l across the parentheses: 36 = 13l - l^2.Quadratic Form: Rearrange the equation into standard quadratic form: 0 = l^2 - 13l + 36.Factor Equation: Factor the quadratic equation: (l - 4)(l - 9) = 0.Solve for l: Solve for l by setting each factor equal to zero: l - 4 = 0 or l - 9 = 0. This gives us two possible values for l: l = 4 or l = 9.Calculate Dimensions: If l = 4, then w = 13 - l = 13 - 4 = 9. If l = 9, then w = 13 - l = 13 - 9 = 4. So the dimensions of the sticker can be either 4 cm by 9 cm or 9 cm by 4 cm.

A rectangular sticker has a perimeter of $26$ centimeters. Its area is $36$ square centimeters. What are the dimensions of the sticker? $\newline$ $\_\_\_$ centimeters by $\_\_\_$ centimeters

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A rectangular sticker has a perimeter of 262626 centimeters. Its area is 363636 square centimeters. What are the dimensions of the sticker?\newline___\_\_\____ centimeters by ___\_\_\____ centimeters

A rectangular sticker has a perimeter of $26$ centimeters. Its area is $36$ square centimeters. What are the dimensions of the sticker? $\newline$ $\_\_\_$ centimeters by $\_\_\_$ centimeters