The area of a rectangular ink pad is 40 square centimeters. The perimeter is 26 centimeters. What are the dimensions of the ink pad? _____ centimeters by _____ centimeters

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The area of a rectangular ink pad is 40 square centimeters.  The perimeter is 26 centimeters. What are the dimensions of the ink pad?  _____ centimeters by _____ centimeters

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Area Equation: Let's denote the length of the ink pad as l and the width as w. The area A of a rectangle is given by the formula A = l * w. Given the area of the ink pad is 40 square centimeters, we can write the equation: 40 = l * wPerimeter Equation: The perimeter P of a rectangle is given by the formula P = 2l + 2w. Given the perimeter of the ink pad is 26 centimeters, we can write the equation: 26 = 2l + 2wSimplify Perimeter Equation: We can simplify the perimeter equation by dividing all terms by 2 to make the equation easier to work with: 26 / 2 = (2l + 2w) / 2 13 = l + w Now we have a simpler linear equation for the perimeter.Substitute and Solve for l: We have two equations now: 1. 40 = l * w (Area equation) 2. 13 = l + w (Perimeter equation)  We can express w from the perimeter equation as w = 13 - l and substitute it into the area equation to find l.Factor Quadratic Equation: Substituting w into the area equation: 40 = l * (13 - l) Expanding the right side of the equation: 40 = 13l - l^2 Rearranging the equation to form a quadratic equation: l^2 - 13l + 40 = 0Solve for l = 5: We can solve the quadratic equation l^2 - 13l + 40 = 0 by factoring: (l - 5)(l - 8) = 0 This gives us two possible solutions for l: l = 5 or l = 8.Solve for l = 8: If l = 5, then substituting back into the perimeter equation 13 = l + w gives us: 13 = 5 + w w = 13 - 5 w = 8Final Dimensions: If l = 8, then substituting back into the perimeter equation 13 = l + w gives us: 13 = 8 + w w = 13 - 8 w = 5We have found two sets of dimensions that satisfy both the area and perimeter equations: 5 cm by 8 cm and 8 cm by 5 cm. Since the order of length and width does not matter for a rectangle, both sets of dimensions are correct.

The area of a rectangular ink pad is $40\,\text{square centimeters}$ . The perimeter is $26\,\text{centimeters}$ . What are the dimensions of the ink pad? $\newline$ $\_\_\_\_$ centimeters by $\_\_\_\_$ centimeters

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The area of a rectangular ink pad is 40 square centimeters40\,\text{square centimeters}40square centimeters. The perimeter is 26 centimeters26\,\text{centimeters}26centimeters. What are the dimensions of the ink pad?\newline____\_\_\_\_____ centimeters by ____\_\_\_\_____ centimeters

The area of a rectangular ink pad is $40\,\text{square centimeters}$ . The perimeter is $26\,\text{centimeters}$ . What are the dimensions of the ink pad? $\newline$ $\_\_\_\_$ centimeters by $\_\_\_\_$ centimeters