The length of the diagonal and the breadth of a rectangle are 17 cm and 8 cm respectively. Find its perimeter (in cm).

Options

A. 92
B. 46
C. 42
D. 84

Answer

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

### Step 1: Identify the given values
- Diagonal (D) = 17 cm
- Breadth (B) = 8 cm

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

### Step 3: Substitute the known values into the equation
We know:
- \( D = 17 \) cm
- \( B = 8 \) cm

Substituting these values into the equation:
\[ 17^2 = L^2 + 8^2 \]

### Step 4: Calculate the squares
Calculate \( 17^2 \) and \( 8^2 \):
- \( 17^2 = 289 \)
- \( 8^2 = 64 \)

### Step 5: Set up the equation
Now, substituting the squared values into the equation:
\[ 289 = L^2 + 64 \]

### Step 6: Solve for L^2
Rearranging the equation to solve for \( L^2 \):
\[ L^2 = 289 - 64 \]
\[ L^2 = 225 \]

### Step 7: Calculate L
Taking the square root of both sides to find L:
\[ L = \sqrt{225} \]
\[ L = 15 \text{ cm} \]

### Step 8: Calculate the perimeter
The formula for the perimeter (P) of a rectangle is:
\[ P = 2(L + B) \]
Substituting the values of L and B:
\[ P = 2(15 + 8) \]
\[ P = 2(23) \]
\[ P = 46 \text{ cm} \]

### Final Answer
The perimeter of the rectangle is **46 cm**.

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