The base of a parallelogram is three times its corresponding height. If the area of the parallel logram is 147 sq. cm, find its base.

Answer

To find the base of the parallelogram given that its base is three times its height and that the area is 147 sq. cm, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables:**
Let the height of the parallelogram be \( h \) cm. According to the problem, the base \( b \) is three times the height.
\[ b = 3h \]

2. **Use the Area Formula:**
The area \( A \) of a parallelogram is given by the formula:
\[ A = \text{base} \times \text{height} \]
Substituting the values we have:
\[ A = b \times h = 147 \, \text{sq. cm} \]

3. **Substitute the Expression for Base:**
Substitute \( b = 3h \) into the area formula:
\[ 3h \times h = 147 \]
This simplifies to:
\[ 3h^2 = 147 \]

4. **Solve for Height:**
Divide both sides by 3:
\[ h^2 = \frac{147}{3} = 49 \]
Now, take the square root of both sides:
\[ h = \sqrt{49} = 7 \, \text{cm} \]

5. **Find the Base:**
Now that we have the height, we can find the base using the relation \( b = 3h \):
\[ b = 3 \times 7 = 21 \, \text{cm} \]

### Final Answer:
The base of the parallelogram is \( 21 \, \text{cm} \).

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