The length of a digonal in cm of a rectangle of length 9 cm and width 6 cm is :
A. `3sqrt(13)`
B. `pm 3sqrt(13)`
C. `3sqrt(5)`
D. `pm 3sqrt(5)`

Options

A. A
B. C
C. D
D. B

Answer

To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. The formula for the diagonal \( d \) of a rectangle with length \( l \) and width \( w \) is given by:

\[ d = \sqrt{l^2 + w^2} \]

### Step 1: Identify the dimensions of the rectangle
The length \( l \) of the rectangle is 9 cm and the width \( w \) is 6 cm.

### Step 2: Substitute the values into the formula
Now we can substitute the values of \( l \) and \( w \) into the formula for the diagonal:

\[ d = \sqrt{9^2 + 6^2} \]

### Step 3: Calculate \( l^2 \) and \( w^2 \)
Calculate \( 9^2 \) and \( 6^2 \):

\[ 9^2 = 81 \]
\[ 6^2 = 36 \]

### Step 4: Add the squares
Now add the two results:

\[ d = \sqrt{81 + 36} \]
\[ d = \sqrt{117} \]

### Step 5: Simplify \( \sqrt{117} \)
Next, we simplify \( \sqrt{117} \):

\[ \sqrt{117} = \sqrt{9 \times 13} = \sqrt{9} \times \sqrt{13} = 3\sqrt{13} \]

### Final Answer
Thus, the length of the diagonal of the rectangle is:

\[ d = 3\sqrt{13} \text{ cm} \]

### Answer Options
From the options given, the correct answer is:
**A. \( 3\sqrt{13} \)**