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

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UpStudy AI · Accepted Answer

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.
Width $$ = 9 $$ km Area $$ = 108 $$ km²

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

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