\#8 The length of a rectangle is \( (3 x-7) \), and the width is twice the value of the length. Find the area of the rectangle. \( (3 x-7)(3 x-7) \)

1. Given the length of the rectangle as \(3x-7\), the width, being twice the length, is: \[ \text{width} = 2(3x-7) = 6x-14. \] 2. The area (\(A\)) of a rectangle is given by: \[ A = \text{length} \times \text{width}. \] 3. Substituting the expressions for length and width: \[ A = (3x-7)(6x-14). \] 4. Notice that the width \(6x-14\) can be factored as: \[ 6x-14 = 2(3x-7). \] 5. Thus, the area becomes: \[ A = (3x-7) \cdot 2(3x-7) = 2(3x-7)^2. \] 6. If desired, you can expand the squared term: \[ (3x-7)^2 = 9x^2 - 42x + 49, \] so that: \[ A = 2(9x^2 - 42x + 49) = 18x^2 - 84x + 98. \] The area of the rectangle is \(2(3x-7)^2\) or, when expanded, \(18x^2 - 84x + 98\).