Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is

Options

A. 25 cm
B. 20 cm
C. 26 cm
D. 3.5 cm

Answer

To find the length of one of the diagonals of a rectangle with sides measuring 10 cm and 24 cm, we can use the Pythagorean theorem. Here’s the step-by-step solution:

### Step 1: Identify the sides of the rectangle
Let the length of the rectangle be \( AB = 24 \, \text{cm} \) and the width be \( BC = 10 \, \text{cm} \).

### Step 2: Understand the diagonal
The diagonal \( AC \) of the rectangle can be considered as the hypotenuse of a right triangle \( ABC \), where \( AB \) and \( BC \) are the two legs.

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides:
\[ AC^2 = AB^2 + BC^2 \]

### Step 4: Substitute the values
Substituting the lengths of the sides into the equation:
\[ AC^2 = (24 \, \text{cm})^2 + (10 \, \text{cm})^2 \]

### Step 5: Calculate the squares
Calculating the squares:
\[ AC^2 = 576 \, \text{cm}^2 + 100 \, \text{cm}^2 \]
\[ AC^2 = 676 \, \text{cm}^2 \]

### Step 6: Find the length of the diagonal
Now, take the square root of both sides to find \( AC \):
\[ AC = \sqrt{676 \, \text{cm}^2} \]
\[ AC = 26 \, \text{cm} \]

### Conclusion
Thus, the length of the diagonal of the rectangle is \( 26 \, \text{cm} \).

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