The area of a parallelogram is `72 cm^2` and its altitude is twice the corresponding base. Then the length of the base is"

Options

A. 3cm
B. 6cm
C. 12cn
D. 8cm

Answer

To find the length of the base of the parallelogram, we can follow these steps:

### Step 1: Understand the formula for the area of a parallelogram.
The area \( A \) of a parallelogram can be calculated using the formula:
\[ A = \text{base} \times \text{height} \]

### Step 2: Assign variables to the base and height.
Let the length of the base be \( x \) cm. According to the problem, the altitude (height) is twice the base. Therefore, the height can be expressed as:
\[ \text{height} = 2x \text{ cm} \]

### Step 3: Substitute the values into the area formula.
Given that the area of the parallelogram is \( 72 \, \text{cm}^2 \), we can substitute the base and height into the area formula:
\[ 72 = x \times (2x) \]

### Step 4: Simplify the equation.
This simplifies to:
\[ 72 = 2x^2 \]

### Step 5: Solve for \( x^2 \).
To isolate \( x^2 \), divide both sides by 2:
\[ x^2 = \frac{72}{2} = 36 \]

### Step 6: Solve for \( x \).
Now, take the square root of both sides to find \( x \):
\[ x = \sqrt{36} = 6 \text{ cm} \]

### Conclusion:
Thus, the length of the base of the parallelogram is \( 6 \, \text{cm} \).

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