One side of a rectangular lawn is 12 m and its diagonal is 13 m . Find the area of the field.

Answer

To find the area of the rectangular lawn, we can follow these steps:

### Step 1: Identify the given values
We know one side (length) of the rectangle is 12 m, and the diagonal (hypotenuse) is 13 m.

### Step 2: Use the Pythagorean theorem to find the other side
In a right triangle, the Pythagorean theorem states that:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides.

Here, let:
- \( a = 12 \) m (one side)
- \( c = 13 \) m (the diagonal)

We need to find \( b \) (the other side).

Using the Pythagorean theorem:
\[ 13^2 = 12^2 + b^2 \]

Calculating the squares:
\[ 169 = 144 + b^2 \]

### Step 3: Solve for \( b^2 \)
Subtract \( 144 \) from both sides:
\[ 169 - 144 = b^2 \]
\[ 25 = b^2 \]

### Step 4: Find \( b \)
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{25} \]
\[ b = 5 \text{ m} \]

### Step 5: Calculate the area of the rectangle
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]
Substituting the values we have:
\[ A = 12 \text{ m} \times 5 \text{ m} \]
\[ A = 60 \text{ m}^2 \]

### Final Answer
The area of the rectangular lawn is \( 60 \text{ m}^2 \).

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