Find the area of a rectangular plot, one side of which is 48 m and its diagonal is 50 m.

Options

A. `372m^(2)`
B. `472m^(2)`
C. `572m^(2)`
D. `672m^(2)`

Answer

To find the area of the rectangular plot, we need to follow these steps:

### Step 1: Identify the given values
We know one side (length) of the rectangle is 48 m, and the diagonal is 50 m.

### Step 2: Use the Pythagorean theorem
In a rectangle, the relationship between the length (L), breadth (B), and diagonal (D) can be expressed using the Pythagorean theorem:
\[ D^2 = L^2 + B^2 \]
Here, \( D = 50 \) m and \( L = 48 \) m.

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 50^2 = 48^2 + B^2 \]

### Step 4: Calculate the squares
Calculate \( 50^2 \) and \( 48^2 \):
\[ 50^2 = 2500 \]
\[ 48^2 = 2304 \]

### Step 5: Set up the equation
Now we can set up the equation:
\[ 2500 = 2304 + B^2 \]

### Step 6: Solve for B²
Rearranging the equation to find \( B^2 \):
\[ B^2 = 2500 - 2304 \]
\[ B^2 = 196 \]

### Step 7: Find B
Now take the square root of both sides to find B:
\[ B = \sqrt{196} \]
\[ B = 14 \, \text{m} \]

### Step 8: Calculate the area of the rectangle
The area (A) of a rectangle is given by the formula:
\[ A = L \times B \]
Substituting the values we have:
\[ A = 48 \times 14 \]

### Step 9: Perform the multiplication
Calculating the area:
\[ A = 672 \, \text{m}^2 \]

### Final Answer
The area of the rectangular plot is:
\[ \text{Area} = 672 \, \text{m}^2 \]

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