The length of the diagonal and the breadth of a rectangle are 29 cm and 20 cm respectively. Find its perimeter (in cm).

Options

A. 164
B. 82
C. 21
D. 42

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Diagonal (d) = 29 cm
- Breadth (b) = 20 cm
- Length (l) = ?

2. **Use the Pythagorean Theorem**:
Since the diagonal, length, and breadth of a rectangle form a right triangle, we can use the Pythagorean theorem:
\[ d^2 = l^2 + b^2 \]
Substituting the known values:
\[ 29^2 = l^2 + 20^2 \]

3. **Calculate the Squares**:
- Calculate \(29^2\):
\[ 29^2 = 841 \]
- Calculate \(20^2\):
\[ 20^2 = 400 \]

4. **Set Up the Equation**:
Substitute the squares into the equation:
\[ 841 = l^2 + 400 \]

5. **Solve for Length (l)**:
Rearranging the equation to solve for \(l^2\):
\[ l^2 = 841 - 400 \]
\[ l^2 = 441 \]
Now, take the square root of both sides to find \(l\):
\[ l = \sqrt{441} = 21 \text{ cm} \]

6. **Calculate the Perimeter**:
The formula for the perimeter (P) of a rectangle is:
\[ P = 2(l + b) \]
Substitute the values of \(l\) and \(b\):
\[ P = 2(21 + 20) \]
\[ P = 2(41) = 82 \text{ cm} \]

### Final Answer:
The perimeter of the rectangle is **82 cm**.

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