If the length of one side and the diagonal of a rectangle are 5 cm and 13 cm respectively, then find its perimeter (in cm).

Options

A. a. 68
B. b. 34
C. c. 25
D. d. 50

Answer

To solve the problem, we need to find the perimeter of a rectangle given one side (breadth) and the diagonal. Here’s a step-by-step solution:

### Step 1: Identify the given values
- One side (breadth) of the rectangle, \( b = 5 \) cm
- Diagonal of the rectangle, \( d = 13 \) cm

### Step 2: Use the Pythagorean theorem
In a rectangle, the diagonal forms a right triangle with the two sides (length and breadth). According to the Pythagorean theorem:
\[ d^2 = l^2 + b^2 \]
where \( l \) is the length and \( b \) is the breadth.

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ 13^2 = l^2 + 5^2 \]
Calculating the squares:
\[ 169 = l^2 + 25 \]

### Step 4: Rearrange the equation to solve for length
Now, we can rearrange the equation to isolate \( l^2 \):
\[ l^2 = 169 - 25 \]
Calculating the right side:
\[ l^2 = 144 \]

### Step 5: Find the length by taking the square root
To find \( l \), take the square root of \( l^2 \):
\[ l = \sqrt{144} = 12 \text{ cm} \]

### Step 6: Calculate the perimeter
The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2(l + b) \]
Substituting the values of \( l \) and \( b \):
\[ P = 2(12 + 5) = 2 \times 17 \]
Calculating the perimeter:
\[ P = 34 \text{ cm} \]

### Final Answer
The perimeter of the rectangle is **34 cm**.

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