Answer :
Final answer:
To find the dimensions of the workbook, we need to solve a system of equations using the given area and perimeter. By setting up two equations, we can determine that the dimensions of the workbook are 6 inches by 10 inches.
Explanation:
To find the dimensions of the workbook, we need to solve a system of equations using the given information. Let's assume the length of the workbook is 'x' inches and the width is 'y' inches. The area of the workbook is given as 54 square inches, so we have the equation xy = 54. The perimeter is given as 30 inches, which can be expressed as 2(x + y) = 30. We now have a system of two equations: xy = 54 and 2(x + y) = 30. Solving this system of equations will give us the dimensions of the workbook.
Start by rearranging the second equation to get x + y = 15. Subtracting this equation from the first equation, we get xy - (x + y) = 54 - 15. Simplifying this equation, we have xy - x - y = 39. Factoring, we get x(y - 1) - (y - 1) = 39. Rearranging again, we have (y - 1)(x - 1) = 39. Since the dimensions of a workbook cannot be negative, we know that y - 1 and x - 1 must both be positive. Now, let's find the factors of 39: 1, 3, 13, and 39. We can substitute these values into the equation (y - 1)(x - 1) = 39 to find the possible values for x and y. After considering all the possibilities, we find that x = 6 and y = 10 (or vice versa) satisfy both equations in the system. Therefore, the dimensions of the workbook are 6 inches by 10 inches.
