ABCD is a square with AB =(x = 16) cm and BC = (3x) cm . The perimeter (in cm ) is

Options

A. 16
B. 24
C. 32
D. 96

Answer

To solve the problem, we need to find the perimeter of square ABCD given the lengths of its sides. Let's break it down step by step.

### Step 1: Understand the properties of the square
In a square, all sides are equal. Therefore, if AB = (x + 16) cm and BC = (3x) cm, we can set these two expressions equal to each other since AB and BC are both sides of the square.

### Step 2: Set up the equation
Since AB = BC, we can write the equation:
\[ x + 16 = 3x \]

### Step 3: Solve for x
To solve for x, we can rearrange the equation:
\[ x + 16 = 3x \]
Subtract \(x\) from both sides:
\[ 16 = 3x - x \]
This simplifies to:
\[ 16 = 2x \]
Now, divide both sides by 2:
\[ x = 8 \]

### Step 4: Find the length of the 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:
\[ \text{Side} = x + 16 = 8 + 16 = 24 \text{ cm} \]

### Step 5: 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:
\[ P = 4 \times 24 = 96 \text{ cm} \]

### Final Answer:
The perimeter of square ABCD is \(96\) cm.

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