he perimeter of a rectangle is 42 km . The length of the rectangle is 12 km . Find the widt nd the area of the rectangle. Width \( = \) Area \( = \) 12 km

To solve the problem, we need to find the width and area of the rectangle given the perimeter and length. ### Step 1: Extract Known Conditions - Perimeter \( P = 42 \) km - Length \( L = 12 \) km ### Step 2: Use the Perimeter Formula The formula for the perimeter of a rectangle is given by: \[ P = 2L + 2W \] where \( W \) is the width. ### Step 3: Substitute Known Values Substituting the known values into the perimeter formula: \[ 42 = 2(12) + 2W \] ### Step 4: Simplify the Equation Calculating \( 2(12) \): \[ 42 = 24 + 2W \] ### Step 5: Solve for Width \( W \) Subtract 24 from both sides: \[ 42 - 24 = 2W \] \[ 18 = 2W \] Now, divide both sides by 2: \[ W = \frac{18}{2} = 9 \text{ km} \] ### Step 6: Calculate the Area The area \( A \) of a rectangle is given by: \[ A = L \times W \] Substituting the values of \( L \) and \( W \): \[ A = 12 \times 9 \] ### Step 7: Perform the Calculation Calculating the area: \[ A = 108 \text{ km}^2 \] ### Final Answers - Width \( W = 9 \) km - Area \( A = 108 \) km² Thus, the width of the rectangle is \( 9 \) km and the area is \( 108 \) km².