The length of one side and the diagonal of a rectangle are 10 cm and 26 cm respectively. Find the length of its other side (in cm).

Options

A. 48
B. 29
C. 24
D. 58

Answer

To find the length of the other side of the rectangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal of the rectangle in this case) is equal to the sum of the squares of the lengths of the other two sides (the length and the breadth of the rectangle).

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of one side (let's call it \( l \)) = 10 cm
- Diagonal (let's call it \( d \)) = 26 cm
- Length of the other side (let's call it \( b \)) = ?

2. **Apply the Pythagorean theorem:**
The relationship can be expressed as:
\[ d^2 = l^2 + b^2 \]

3. **Substitute the known values into the equation:**
\[ 26^2 = 10^2 + b^2 \]

4. **Calculate the squares:**
\[ 676 = 100 + b^2 \]

5. **Isolate \( b^2 \):**
Subtract 100 from both sides:
\[ 676 - 100 = b^2 \]
\[ 576 = b^2 \]

6. **Take the square root of both sides to find \( b \):**
\[ b = \sqrt{576} \]
\[ b = 24 \text{ cm} \]

### Final Answer:
The length of the other side of the rectangle is **24 cm**.