The perimeter of an airplane ticket is 34 centimeters. The area is 70 square centimeters. What are the dimensions of the ticket? _____ centimeters by _____ centimeters

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The perimeter of an airplane ticket is 34 centimeters.  The area is 70 square centimeters. What are the dimensions of the ticket?  _____ centimeters by _____ centimeters

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Define Variables: Let l be the length and w be the width of the airplane ticket. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w.Perimeter Equation: Given the perimeter of the airplane ticket is 34 centimeters, we can write the equation 34 = 2l + 2w.Simplify Perimeter: Simplify the perimeter equation by dividing all terms by 2 to get 17 = l + w.Area Equation: The area (A) of a rectangle is given by the formula A = lw. Given the area of the airplane ticket is 70 square centimeters, we can write the equation 70 = lw.Solve System of Equations: We now have a system of two equations with two variables: 1. 17 = l + w 2. 70 = 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 w in terms of l: From the first equation, express w in terms of l: w = 17 - l.Substitute into Area Equation: Substitute w = 17 - l into the second equation 70 = lw to get 70 = l(17 - l).Expand Quadratic Equation: Expand the equation 70 = 17l - l^2 to form a quadratic equation 0 = l^2 - 17l + 70.Factor Quadratic Equation: Factor the quadratic equation l^2 - 17l + 70 = 0 to find the values of l. The factors of 70 that add up to 17 are 10 and 7, so the factored form is (l - 10)(l - 7) = 0.Solve for l: Solve for l by setting each factor equal to zero: l - 10 = 0 or l - 7 = 0. This gives us two possible values for l: l = 10 or l = 7.Find Possible Dimensions: If l = 10, then w = 17 - l = 17 - 10 = 7. If l = 7, then w = 17 - l = 17 - 7 = 10. Since a rectangle's length and width are interchangeable, the dimensions of the ticket can be 10 centimeters by 7 centimeters or 7 centimeters by 10 centimeters.

The perimeter of an airplane ticket is $34$ centimeters. The area is $70$ square centimeters. What are the dimensions of the ticket? $\newline$ $\_\_\_$ centimeters by $\_\_\_$ centimeters

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The perimeter of an airplane ticket is 343434 centimeters. The area is 707070 square centimeters. What are the dimensions of the ticket?\newline___\_\_\____ centimeters by ___\_\_\____ centimeters

The perimeter of an airplane ticket is $34$ centimeters. The area is $70$ square centimeters. What are the dimensions of the ticket? $\newline$ $\_\_\_$ centimeters by $\_\_\_$ centimeters