The area of a parallelogrma is 288 sq. m. Find the base given that its height is half its base.

Answer

To solve the problem, we need to find the base of a parallelogram given that its area is 288 sq. m and its height is half of its base. Let's break down the solution step by step.

### Step 1: Understand the relationship between area, base, and height
The area \( A \) of a parallelogram can be calculated using the formula:
\[ A = \text{base} \times \text{height} \]
We know the area is 288 sq. m.

### Step 2: Define the variables
Let the base of the parallelogram be \( b \). According to the problem, the height \( h \) is half of the base:
\[ h = \frac{b}{2} \]

### Step 3: Substitute the height into the area formula
Now, we can substitute the expression for height into the area formula:
\[ 288 = b \times \frac{b}{2} \]

### Step 4: Simplify the equation
This simplifies to:
\[ 288 = \frac{b^2}{2} \]

To eliminate the fraction, multiply both sides by 2:
\[ 576 = b^2 \]

### Step 5: Solve for the base
Now, we need to find \( b \) by taking the square root of both sides:
\[ b = \sqrt{576} \]

### Step 6: Calculate the square root
Calculating the square root:
\[ b = 24 \]

### Conclusion
The base of the parallelogram is:
\[ \text{Base} = 24 \text{ m} \]