The surface of an air hockey table has an area of 40 square feet and a perimeter of 28 feet. What are the dimensions of the air hockey table? _____ feet by _____ feet

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The surface of an air hockey table has an area of 40 square feet and a perimeter of 28 feet. What are the dimensions of the air hockey table?  _____ feet by _____ feet

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Define Area Formula:  Let l and w be the length and width of the air hockey table, respectively. The area of a rectangle is given by A = l * w. Substitute Area Value:  Given area A = 40 square feet. Substitute into the area formula: 40 = l * w. Define Perimeter Formula:  The perimeter of a rectangle is given by P = 2l + 2w. Given perimeter P = 28 feet. Substitute into the perimeter formula: 28 = 2l + 2w. Substitute Perimeter Value:  Simplify the perimeter equation: 14 = l + w. Simplify Perimeter Equation:  We now have two equations: 40 = l * w and 14 = l + w. Solve these equations simultaneously. Solve Equations Simultaneously:  Substitute w = 14 - l into the area equation: 40 = l * (14 - l). Substitute Width into Area Equation:  Expand and rearrange the equation: 40 = 14l - l^2. Rearrange to form a quadratic equation: l^2 - 14l + 40 = 0. Expand and Rearrange Equation:  Solve the quadratic equation using the quadratic formula, l = (-b ± sqrt(b^2 - 4ac)) / 2a. Here, a = 1, b = -14, and c = 40. Solve Quadratic Equation:  Calculate the discriminant: (-14)^2 - 4*1*40 = 196 - 160 = 36. Calculate Discriminant:  Calculate the roots: l = (14 ± sqrt(36)) / 2. So, l = (14 ± 6) / 2. Calculate Roots:  This gives l = 10 or l = 4. If l = 10, then w = 14 - 10 = 4. If l = 4, then w = 14 - 4 = 10.

The surface of an air hockey table has an area of $40$ square feet and a perimeter of $28$ feet. What are the dimensions of the air hockey table? $\newline$ $\_\_\_$ feet by $\_\_\_$ feet

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The surface of an air hockey table has an area of 404040 square feet and a perimeter of 282828 feet. What are the dimensions of the air hockey table?\newline___\_\_\____ feet by ___\_\_\____ feet

The surface of an air hockey table has an area of $40$ square feet and a perimeter of $28$ feet. What are the dimensions of the air hockey table? $\newline$ $\_\_\_$ feet by $\_\_\_$ feet