The area of a parallelogram is `338 m^(2)` . If its altitude is twice the corresponding base,find the base and the altitude.

Answer

To solve the problem step by step, we will use the information given in the question about the area of the parallelogram and the relationship between the base and the altitude.

### Step-by-Step Solution:

1. **Understand the formula for the area of a parallelogram**:
The area \( A \) of a parallelogram is given by the formula:
\[ A = \text{base} \times \text{height} \]

2. **Set up the equation with given values**:
We know from the problem that the area \( A \) is \( 338 \, m^2 \). Let the base be \( b \) and the height (altitude) be \( h \). According to the problem, the altitude is twice the base, which can be expressed as:
\[ h = 2b \]
Now, substituting this into the area formula:
\[ 338 = b \times h \]
Replacing \( h \) with \( 2b \):
\[ 338 = b \times (2b) \]
This simplifies to:
\[ 338 = 2b^2 \]

3. **Solve for \( b^2 \)**:
To isolate \( b^2 \), divide both sides by 2:
\[ b^2 = \frac{338}{2} = 169 \]

4. **Find the value of \( b \)**:
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{169} = 13 \, m \]

5. **Calculate the height \( h \)**:
Since we know that \( h = 2b \):
\[ h = 2 \times 13 = 26 \, m \]

6. **Final results**:
The base of the parallelogram is \( 13 \, m \) and the altitude is \( 26 \, m \).

### Summary:
- Base \( b = 13 \, m \)
- Height (altitude) \( h = 26 \, m \)