The length and breadth of a rectangle are 24 cm and 7 cm respectively. What must be the length of its diagonal (in cm.) ?

Options

A. 50
B. 25
C. 28
D. 56

Answer

To find the length of the diagonal of a rectangle with given length and breadth, we can use the Pythagorean theorem. Here’s how to solve the problem step by step:

### Step 1: Identify the dimensions of the rectangle
The length (l) of the rectangle is given as 24 cm, and the breadth (b) is given as 7 cm.

### Step 2: Use the Pythagorean theorem
In a rectangle, the diagonal (d) can be found using the formula:
\[ d = \sqrt{l^2 + b^2} \]

### Step 3: Substitute the values into the formula
Now, substitute the values of length and breadth into the formula:
\[ d = \sqrt{(24)^2 + (7)^2} \]

### Step 4: Calculate the squares
Calculate \( 24^2 \) and \( 7^2 \):
- \( 24^2 = 576 \)
- \( 7^2 = 49 \)

### Step 5: Add the squares
Now, add the two results:
\[ 576 + 49 = 625 \]

### Step 6: Take the square root
Now, take the square root of the sum:
\[ d = \sqrt{625} = 25 \]

### Final Result
The length of the diagonal of the rectangle is **25 cm**.

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