Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 feet

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Define Perimeter Formula: Let l be the length and w be the width of the rectangular lawn. The perimeter of a rectangle is given by the formula P = 2l + 2w.Perimeter Equation: Given the perimeter of the rectangular lawn is 100 feet, we can write the equation: 100 = 2l + 2wSimplify Perimeter: Simplify the perimeter equation by dividing all terms by 2: 50 = l + wDefine Area Formula: The area of a rectangle is given by the formula A = lw. Given the area of the rectangular lawn is 600 square feet, we can write the equation: 600 = lwArea Equation: We now have a system of two equations with two variables: 50 = l + w (Equation 1) 600 = lw (Equation 2) We can solve this system by expressing one variable in terms of the other using Equation 1 and then substituting into Equation 2.Solve System of Equations: From Equation 1, express w in terms of l: w = 50 - lExpress w in terms of l: Substitute w = 50 - l into Equation 2: 600 = l(50 - l)Substitute into Equation 2: Expand the equation and rearrange it into a quadratic equation: 600 = 50l - l^2 0 = l^2 - 50l + 600Expand and Rearrange: Factor the quadratic equation: 0 = (l - 20)(l - 30)Factor Quadratic Equation: Solve for l by setting each factor equal to zero: l - 20 = 0 or l - 30 = 0 l = 20 or l = 30Solve for l: If l = 20, then w = 50 - l = 50 - 20 = 30. If l = 30, then w = 50 - l = 50 - 30 = 20. So, the length and width of the lawn can be either (20, 30) or (30, 20) feet.

Find the dimensions of a rectangular lawn whose perimeter is $100$ feet and whose area is $600$ square feet

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Find the dimensions of a rectangular lawn whose perimeter is $100$ feet and whose area is $600$ square feet