A map of the world has a perimeter of 20 feet. Its area is 21 square feet. What are the dimensions of the map? _____ feet by _____ feet

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A map of the world has a perimeter of 20 feet.  Its area is 21 square feet. What are the dimensions of the map?  _____ feet by _____ feet

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Perimeter Formula: Let l be the length and w be the width of the map. The perimeter of a rectangle is given by the formula P = 2l + 2w.Perimeter Equation: Given the perimeter of the map is 20 feet, we can write the equation 20 = 2l + 2w.Simplify Equation: Simplify the perimeter equation by dividing all terms by 2 to get 10 = l + w.Area Formula: The area of a rectangle is given by the formula A = lw. Given the area of the map is 21 square feet, we can write the equation 21 = lw.System of Equations: We now have a system of two equations with two variables: 1. 10 = l + w 2. 21 = lw  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 Width in Terms of Length: From the first equation, express w in terms of l: w = 10 - l.Substitute Width into Equation: Substitute w = 10 - l into the second equation: 21 = l(10 - l).Expand Equation: Expand the equation: 21 = 10l - l^2.Rearrange Equation: Rearrange the equation to form a quadratic equation: l^2 - 10l + 21 = 0.Factor Quadratic Equation: Factor the quadratic equation: (l - 7)(l - 3) = 0.Solve for Length: Solve for l: l = 7 or l = 3. Since l and w are interchangeable as length and width, we can have two solutions: l = 7 and w = 3, or l = 3 and w = 7.Check Solutions: Check the solutions with the original equations to ensure they satisfy both the perimeter and area. For l = 7 and w = 3: P = 2(7) + 2(3) = 14 + 6 = 20 and A = 7 * 3 = 21. For l = 3 and w = 7: P = 2(3) + 2(7) = 6 + 14 = 20 and A = 3 * 7 = 21. Both solutions satisfy the original equations.

A map of the world has a perimeter of $20$ feet. Its area is $21$ square feet. What are the dimensions of the map? $\newline$ $\_\_\_$ feet by $\_\_\_$ feet

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A map of the world has a perimeter of $20$ feet. Its area is $21$ square feet. What are the dimensions of the map? $\newline$ $\_\_\_$ feet by $\_\_\_$ feet