The length of the diagonal and the breadth of a rectangle is 25 and 7 cm respectively. Calculate its area (in `cm^(2)`).

Options

A. a)336
B. b)168
C. c)240
D. d)480

Answer

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

### Step 1: Understand the given information
We have the length of the diagonal (d) = 25 cm and the breadth (b) = 7 cm of the rectangle.

### Step 2: Use the Pythagorean theorem
In a rectangle, the diagonal, length (l), and breadth (b) are related by the Pythagorean theorem:
\[ d^2 = l^2 + b^2 \]
Where:
- \( d \) = diagonal
- \( l \) = length
- \( b \) = breadth

### Step 3: Substitute the known values
We know:
- \( d = 25 \) cm
- \( b = 7 \) cm

Substituting these values into the equation:
\[ 25^2 = l^2 + 7^2 \]

### Step 4: Calculate the squares
Calculating the squares:
\[ 625 = l^2 + 49 \]

### Step 5: Solve for the length
Now, we can isolate \( l^2 \):
\[ l^2 = 625 - 49 \]
\[ l^2 = 576 \]

Taking the square root to find \( l \):
\[ l = \sqrt{576} \]
\[ l = 24 \text{ cm} \]

### Step 6: Calculate the area of the rectangle
The area \( A \) of a rectangle is given by:
\[ A = l \times b \]
Substituting the values we found:
\[ A = 24 \times 7 \]

### Step 7: Perform the multiplication
Calculating the area:
\[ A = 168 \text{ cm}^2 \]

### Final Answer
The area of the rectangle is \( 168 \text{ cm}^2 \).

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