The length of the diagonal and the breadth of a rectangle is 29 cm and 20 cm respectively. Calculate its area `("in cm"^2).`

Options

A. 840
B. 160
C. 320
D. 420

Answer

To find the area of the rectangle given the length of the diagonal and the breadth, we can follow these steps:

### Step 1: Identify the given values
- Diagonal (d) = 29 cm
- Breadth (b) = 20 cm

### Step 2: Use the Pythagorean theorem
In a rectangle, the diagonal, breadth, and length form a right triangle. According to the Pythagorean theorem:

\[ d^2 = b^2 + l^2 \]

Where:
- \( d \) is the diagonal,
- \( b \) is the breadth,
- \( l \) is the length.

### Step 3: Substitute the known values into the equation
Substituting the values we have:

\[ 29^2 = 20^2 + l^2 \]

### Step 4: Calculate the squares
Calculating the squares:

\[ 841 = 400 + l^2 \]

### Step 5: Solve for the length (l)
Rearranging the equation to solve for \( l^2 \):

\[ l^2 = 841 - 400 \]
\[ l^2 = 441 \]

Now, take the square root to find \( l \):

\[ l = \sqrt{441} \]
\[ l = 21 \, \text{cm} \]

### Step 6: Calculate the area of the rectangle
The area \( A \) of a rectangle is given by the formula:

\[ A = l \times b \]

Substituting the values of length and breadth:

\[ A = 21 \, \text{cm} \times 20 \, \text{cm} \]
\[ A = 420 \, \text{cm}^2 \]

### Final Answer
The area of the rectangle is \( 420 \, \text{cm}^2 \).

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