ABCD is a square with AB = (x + 6) cm and BC= (3x) cm. The perimeter (in cm) is

Options

A. 16
B. 24
C. 32
D. 36

Answer

To find the perimeter of square ABCD, we need to follow these steps:

### Step 1: Set the sides equal
Since ABCD is a square, all sides are equal. We have:
- AB = (x + 6) cm
- BC = (3x) cm

Thus, we can set the two expressions for the sides equal to each other:
\[ x + 6 = 3x \]

### Step 2: Solve for x
Now, we will solve the equation from Step 1:
1. Rearranging the equation gives:
\[ 6 = 3x - x \]
2. Simplifying this, we get:
\[ 6 = 2x \]
3. Dividing both sides by 2:
\[ x = \frac{6}{2} = 3 \text{ cm} \]

### Step 3: Find the length of a side of the square
Now that we have the value of x, we can find the length of one side of the square. We can use either expression for the side. Let's use BC:
\[ BC = 3x = 3 \times 3 = 9 \text{ cm} \]

### Step 4: Calculate the perimeter
The perimeter (P) of a square is given by the formula:
\[ P = 4 \times \text{side} \]
Substituting the side length we found:
\[ P = 4 \times 9 = 36 \text{ cm} \]

### Final Answer
The perimeter of square ABCD is **36 cm**.

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