The area of a triangle with base x unit is equal to the area of a square with sie x sq unit. Then , the altitude of the triangle is

Options

A. x unit
B. 2 x unit
C. 3x unit
D. x/2 unit

Answer

To find the altitude of the triangle given that the area of the triangle with base \( x \) units is equal to the area of a square with side \( x \) square units, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Area of the Triangle:**
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, the base is \( x \) units and we will denote the height (altitude) as \( h \).

2. **Setting Up the Equation for the Triangle:**
Substituting the values into the area formula for the triangle, we get:
\[ A_{\text{triangle}} = \frac{1}{2} \times x \times h \]

3. **Understanding the Area of the Square:**
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Since the side of the square is \( x \) units, the area of the square is:
\[ A_{\text{square}} = x^2 \]

4. **Setting the Areas Equal:**
According to the problem, the area of the triangle is equal to the area of the square:
\[ \frac{1}{2} \times x \times h = x^2 \]

5. **Solving for the Height \( h \):**
To find \( h \), we can rearrange the equation:
\[ h = \frac{x^2 \times 2}{x} \]
Simplifying this gives:
\[ h = 2x \]

### Final Answer:
The altitude of the triangle is \( 2x \) units.