The perimeter of an envelope is 28 inches. The area is 40 square inches. What are the dimensions of the envelope? _____ inches by _____ inches

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The perimeter of an envelope is 28 inches.  The area is 40 square inches. What are the dimensions of the envelope?  _____ inches by _____ inches

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Define Variables: Let's denote the length of the envelope as l inches and the width as w inches. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w.Perimeter Equation: Given the perimeter of the envelope is 28 inches, we can write the equation 2l + 2w = 28.Simplify Equation: We can simplify this equation by dividing all terms by 2, which gives us l + w = 14.Area Formula: The area (A) of a rectangle is given by the formula A = lw.Area Equation: Given the area of the envelope is 40 square inches, we can write the equation lw = 40.Solve System of Equations: Now we have a system of two equations with two variables: 1. l + w = 14 2. lw = 40 We can solve this system by expressing one variable in terms of the other using the first equation and then substituting into the second equation.Express w in terms of l: Let's express w in terms of l from the first equation: w = 14 - l.Substitute into Equation: Substitute w = 14 - l into the second equation lw = 40: l(14 - l) = 40Expand Equation: Expand the equation: 14l - l^2 = 40.Rearrange Equation: Rearrange the equation to form a quadratic equation: l^2 - 14l + 40 = 0.Factor Quadratic Equation: Factor the quadratic equation: (l - 10)(l - 4) = 0.Solve for l: Set each factor equal to zero and solve for l: 1. l - 10 = 0 gives l = 10 2. l - 4 = 0 gives l = 4Find Solutions: Since l and w are interchangeable as length and width, we can have two solutions: 1. l = 10 inches and w = 4 inches 2. l = 4 inches and w = 10 inches Both sets of dimensions satisfy the given perimeter and area.

The perimeter of an envelope is $28$ inches. The area is $40$ square inches. What are the dimensions of the envelope? $\newline$ $\_\_\_\_$ inches by $\_\_\_\_$ inches

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The perimeter of an envelope is 282828 inches. The area is 404040 square inches. What are the dimensions of the envelope?\newline____\_\_\_\_____ inches by ____\_\_\_\_____ inches

The perimeter of an envelope is $28$ inches. The area is $40$ square inches. What are the dimensions of the envelope? $\newline$ $\_\_\_\_$ inches by $\_\_\_\_$ inches