The area of a square is `16200 m^(2)`. Find the length of its diagonal.

Options

A. 170m
B. 180m
C. 160m
D. 280m

Answer

To find the length of the diagonal of a square when the area is given, we can follow these steps:

### Step 1: Understand the relationship between area and side length of a square.
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
where "side" is the length of one side of the square.

### Step 2: Set up the equation using the given area.
Given that the area of the square is \( 16200 \, m^2 \), we can write:
\[ \text{side}^2 = 16200 \]

### Step 3: Solve for the side length.
To find the side length, we take the square root of both sides:
\[ \text{side} = \sqrt{16200} \]

### Step 4: Simplify the square root.
To simplify \( \sqrt{16200} \), we can factor it:
\[ 16200 = 162 \times 100 = 162 \times 10^2 \]
Now, we can break down \( 162 \):
\[ 162 = 81 \times 2 = 9^2 \times 2 \]
Thus,
\[ 16200 = 9^2 \times 2 \times 10^2 \]
Now, taking the square root:
\[ \sqrt{16200} = \sqrt{9^2 \times 2 \times 10^2} = 9 \times 10 \times \sqrt{2} = 90\sqrt{2} \]
So, the side length of the square is:
\[ \text{side} = 90\sqrt{2} \, m \]

### Step 5: Find the length of the diagonal.
The diagonal \( d \) of a square can be found using the formula:
\[ d = \text{side} \times \sqrt{2} \]
Substituting the value of the side:
\[ d = 90\sqrt{2} \times \sqrt{2} = 90 \times 2 = 180 \, m \]

### Final Answer:
The length of the diagonal of the square is \( 180 \, m \).

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