Points] DETAILS MY NOTES TGEIALG6 2.5 .055 . The length of a picture is 6.75 inches shorter than twice the width. If the perimeter of the picture is 118.5 inches, find its dimension width length SUBMIT ANSWER

Let the width be \( w \) and the length be \( l \). 1. The length is 6.75 inches shorter than twice the width, so: \[ l = 2w - 6.75 \] 2. The perimeter of the rectangle is given by: \[ P = 2(l + w) = 118.5 \] Dividing both sides by 2, we obtain: \[ l + w = 59.25 \] 3. Substitute the expression for \( l \) from step 1 into the perimeter equation: \[ (2w - 6.75) + w = 59.25 \] Combine like terms: \[ 3w - 6.75 = 59.25 \] 4. Solve for \( w \) by adding 6.75 to both sides: \[ 3w = 59.25 + 6.75 = 66 \] Then, divide both sides by 3: \[ w = \frac{66}{3} = 22 \] 5. Now, substitute \( w = 22 \) back into the expression for \( l \): \[ l = 2(22) - 6.75 = 44 - 6.75 = 37.25 \] The dimensions of the picture are: - Width: \( 22 \) inches - Length: \( 37.25 \) inches