\( \square x= \) width length \( =x+3 \)

It looks like you're describing a geometric shape—possibly a rectangle—where you have: - **Width**: \( x \) - **Length**: \( x + 3 \) Assuming you're referring to a **rectangle**, here's how you can work with these dimensions: ### 1. Area of the Rectangle The area (\( A \)) of a rectangle is calculated by multiplying its width by its length. \[ A = \text{Width} \times \text{Length} = x \times (x + 3) = x^2 + 3x \] ### 2. Perimeter of the Rectangle The perimeter (\( P \)) is the sum of all sides of the rectangle. Since opposite sides are equal: \[ P = 2 \times (\text{Width} + \text{Length}) = 2(x) + 2(x + 3) = 2x + 2x + 6 = 4x + 6 \] ### 3. Solving for \( x \) If you have additional information, such as the area or perimeter, you can solve for \( x \). For example: #### **a. Given the Area** Suppose the area is 30 square units: \[ x^2 + 3x = 30 \\ x^2 + 3x - 30 = 0 \] Solve the quadratic equation: \[ x = \frac{-3 \pm \sqrt{9 + 120}}{2} = \frac{-3 \pm \sqrt{129}}{2} \] Since length can't be negative: \[ x = \frac{-3 + \sqrt{129}}{2} \approx \frac{-3 + 11.36}{2} \approx 4.18 \text{ units} \] #### **b. Given the Perimeter** Suppose the perimeter is 22 units: \[ 4x + 6 = 22 \\ 4x = 16 \\ x = 4 \text{ units} \] Then, the length would be: \[ x + 3 = 4 + 3 = 7 \text{ units} \] ### 4. Visual Representation Here's a simple diagram to illustrate the rectangle: ``` +---------------------+ | | | | Length = x + 3 | | +---------------------+ Width = x ``` ### 5. Summary - **Width**: \( x \) - **Length**: \( x + 3 \) - **Area**: \( x^2 + 3x \) - **Perimeter**: \( 4x + 6 \) If you provide more context or additional information (like a specific value for area or perimeter), I can help you solve for \( x \) or address any other related questions you might have!