In a rectangle, length=8 cm, breadth = 6cm. Then its diagonal is:

Options

A. 9 cm
B. 14 cm
C. 10 cm
D. 12 cm

Answer

To find the length of the diagonal of a rectangle with length 8 cm and breadth 6 cm, we can use the Pythagorean theorem. Here’s the step-by-step solution:

### Step 1: Identify the dimensions of the rectangle
The length (l) of the rectangle is given as 8 cm and the breadth (b) is given as 6 cm.

### Step 2: Understand the relationship in a rectangle
In a rectangle, the diagonal (d) can be found using the Pythagorean theorem. The diagonal forms a right triangle with the length and breadth as the two other sides.

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ d^2 = l^2 + b^2 \]
Where:
- \( d \) is the diagonal,
- \( l \) is the length,
- \( b \) is the breadth.

### Step 4: Substitute the values into the formula
Substituting the values of length and breadth into the formula:
\[ d^2 = (8 \, \text{cm})^2 + (6 \, \text{cm})^2 \]

### Step 5: Calculate the squares
Calculating the squares:
\[ d^2 = 64 \, \text{cm}^2 + 36 \, \text{cm}^2 \]

### Step 6: Add the squares
Adding the results:
\[ d^2 = 100 \, \text{cm}^2 \]

### Step 7: Find the diagonal
To find \( d \), take the square root of both sides:
\[ d = \sqrt{100 \, \text{cm}^2} \]
\[ d = 10 \, \text{cm} \]

### Final Answer
The length of the diagonal of the rectangle is **10 cm**.

---