The base of a parallelogram is three times its height. If the area of the parallelogram is 75 sq cm, then its height is

Options

A. 5 cm
B. `5 sqrt(2)` cm
C. `3 sqrt(2)` cm
D. 15 cm

Answer

To find the height of the parallelogram given that the base is three times its height and the area is 75 sq cm, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables:**
- Let the height of the parallelogram be denoted as \( h \).
- According to the problem, the base \( b \) is three times the height, so we can express the base as:
\[ b = 3h \]

2. **Use the Area Formula:**
- The area \( A \) of a parallelogram is given by the formula:
\[ A = b \times h \]
- We know from the problem that the area \( A \) is 75 sq cm. Therefore, we can substitute the expression for \( b \) into the area formula:
\[ 75 = (3h) \times h \]

3. **Set Up the Equation:**
- This simplifies to:
\[ 75 = 3h^2 \]

4. **Solve for \( h^2 \):**
- To isolate \( h^2 \), divide both sides of the equation by 3:
\[ h^2 = \frac{75}{3} \]
\[ h^2 = 25 \]

5. **Find the Height \( h \):**
- Now, take the square root of both sides to find \( h \):
\[ h = \sqrt{25} \]
\[ h = 5 \text{ cm} \]

### Final Answer:
The height of the parallelogram is \( 5 \) cm.

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