The length of the diagonal and the breadth of a rectangle are 25 cm and 7 cm respectively. Find its perimeter (in cm).

Options

A. 124
B. 41
C. 82
D. 62

Answer

To find the perimeter 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) = 25 cm
- Breadth (b) = 7 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:
- \( d \) = diagonal
- \( b \) = breadth
- \( L \) = length

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 25^2 = 7^2 + L^2 \]

### Step 4: Calculate the squares
Calculate \( 25^2 \) and \( 7^2 \):
\[ 625 = 49 + L^2 \]

### Step 5: Rearrange the equation to solve for L
Subtract 49 from both sides:
\[ L^2 = 625 - 49 \]
\[ L^2 = 576 \]

### Step 6: Take the square root to find L
Now, take the square root of both sides:
\[ L = \sqrt{576} \]
\[ L = 24 \, \text{cm} \]

### Step 7: Calculate the perimeter
The formula for the perimeter (P) of a rectangle is:
\[ P = 2(L + b) \]
Substituting the values of L and b:
\[ P = 2(24 + 7) \]
\[ P = 2(31) \]
\[ P = 62 \, \text{cm} \]

### Final Answer
The perimeter of the rectangle is **62 cm**.

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