The length of one side and the diagonal of a rectangle are 20 cm and 29 cm respectively. Find the length of its other side (in cm).

Options

A. A. 42
B. B. 30
C. C. 21
D. D. 60

Answer

To solve the problem step by step, we will use the Pythagorean theorem, which relates the sides of a right triangle.

### Step-by-Step Solution:

1. **Identify the given values**:
- One side of the rectangle (let's call it width) = 20 cm
- Diagonal of the rectangle = 29 cm
- Let the other side of the rectangle (length) be denoted as \( x \).

2. **Apply the Pythagorean theorem**:
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides. This can be expressed as:
\[ \text{Diagonal}^2 = \text{Width}^2 + \text{Length}^2 \]
Substituting the known values:
\[ 29^2 = 20^2 + x^2 \]

3. **Calculate the squares**:
- Calculate \( 29^2 \):
\[ 29^2 = 841 \]
- Calculate \( 20^2 \):
\[ 20^2 = 400 \]

4. **Set up the equation**:
Substitute the squares back into the equation:
\[ 841 = 400 + x^2 \]

5. **Isolate \( x^2 \)**:
To find \( x^2 \), subtract 400 from both sides:
\[ x^2 = 841 - 400 \]
\[ x^2 = 441 \]

6. **Take the square root**:
To find \( x \), take the square root of both sides:
\[ x = \sqrt{441} \]
\[ x = 21 \]

7. **Conclusion**:
The length of the other side of the rectangle is 21 cm.

### Final Answer:
The length of the other side is **21 cm**.

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