The area of a rectangular ink pad is 48 square centimeters. The perimeter is 28 centimeters. What are the dimensions of the ink pad? _____ centimeters by _____ centimeters

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The area of a rectangular ink pad is 48 square centimeters.  The perimeter is 28 centimeters. What are the dimensions of the ink pad?  _____ centimeters by _____ centimeters

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Define Variables: Let l be the length and w be the width of the rectangular ink pad. The area of a rectangle is given by the formula A = l * w.Area and Perimeter Formulas: The area of the ink pad is given as 48 square centimeters. Substitute 48 for A in the area formula. 48 = l * wEquations Setup: The perimeter of a rectangle is given by the formula P = 2l + 2w. The perimeter of the ink pad is given as 28 centimeters. Substitute 28 for P in the perimeter formula. 28 = 2l + 2wSolve Simultaneously: Divide the perimeter equation by 2 to simplify. 28 / 2 = (2l + 2w) / 2 14 = l + wRearrange Perimeter Equation: We now have two equations with two variables: 48 = l * w (Area equation) 14 = l + w (Perimeter equation) We can solve these equations simultaneously to find the values of l and w.Substitute and Expand: Rearrange the perimeter equation to express one variable in terms of the other. w = 14 - lQuadratic Equation: Substitute w = 14 - l into the area equation. 48 = l * (14 - l)Factorize: Expand the equation and form a quadratic equation. 48 = 14l - l^2 Move all terms to one side to set the equation to zero. l^2 - 14l + 48 = 0Solve for Length: Factor the quadratic equation. (l - 6)(l - 8) = 0Final Solutions: Solve for l by setting each factor equal to zero. l - 6 = 0 or l - 8 = 0 l = 6 or l = 8If l = 6, then w = 14 - l = 14 - 6 = 8. If l = 8, then w = 14 - l = 14 - 8 = 6. Both pairs (6, 8) and (8, 6) are valid solutions since a rectangle can have its length and width interchanged.

The area of a rectangular ink pad is $48\,\text{square centimeters}$ . The perimeter is $28\,\text{centimeters}$ . What are the dimensions of the ink pad? $\newline$ $\_\_\_\_$ centimeters by $\_\_\_\_$ centimeters

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The area of a rectangular ink pad is 48 square centimeters48\,\text{square centimeters}48square centimeters. The perimeter is 28 centimeters28\,\text{centimeters}28centimeters. What are the dimensions of the ink pad?\newline____\_\_\_\_____ centimeters by ____\_\_\_\_____ centimeters

The area of a rectangular ink pad is $48\,\text{square centimeters}$ . The perimeter is $28\,\text{centimeters}$ . What are the dimensions of the ink pad? $\newline$ $\_\_\_\_$ centimeters by $\_\_\_\_$ centimeters