One side of a rectangular field is 4 metres and its diagonal is 5 metres. The area of the field is

Options

A. `12m^2`
B. `20m^2`
C. `15m^2`
D. `sqrt5m^2`

Answer

To find the area of the rectangular field given one side and the diagonal, we can follow these steps:

### Step 1: Identify the given values
We know:
- One side of the rectangle (let's call it length \( l \)) = 4 meters
- Diagonal of the rectangle (let's call it \( d \)) = 5 meters

### Step 2: Use the Pythagorean theorem
In a rectangle, the diagonal can be calculated using the Pythagorean theorem:
\[ d^2 = l^2 + w^2 \]
where \( w \) is the width of the rectangle.

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 5^2 = 4^2 + w^2 \]
This simplifies to:
\[ 25 = 16 + w^2 \]

### Step 4: Solve for \( w^2 \)
Rearranging the equation to find \( w^2 \):
\[ w^2 = 25 - 16 \]
\[ w^2 = 9 \]

### Step 5: Find \( w \)
Taking the square root of both sides gives us:
\[ w = \sqrt{9} = 3 \text{ meters} \]

### Step 6: Calculate the area of the rectangle
The area \( A \) of a rectangle is given by the formula:
\[ A = l \times w \]
Substituting the values we have:
\[ A = 4 \times 3 = 12 \text{ square meters} \]

### Final Answer
The area of the rectangular field is **12 square meters**.

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