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

Options

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

Answer

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

### Step 1: Understand the Area of the Square
The area of a square with side length \( x \) is given by the formula:
\[ \text{Area of square} = \text{side}^2 = x^2 \]

### Step 2: Write the Area of the Triangle
The area of a triangle can be calculated using the formula:
\[ \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, the base of the triangle is \( x \) units. Let the height (or altitude) be \( h \) units. Thus, the area of the triangle becomes:
\[ \text{Area of triangle} = \frac{1}{2} \times x \times h \]

### Step 3: Set the Areas Equal
According to the problem, the area of the triangle is equal to the area of the square. Therefore, we can set the two areas equal to each other:
\[ \frac{1}{2} \times x \times h = x^2 \]

### Step 4: Solve for the Altitude (h)
To find the altitude \( h \), we can rearrange the equation:
\[ h = \frac{x^2}{\frac{1}{2} \times x} \]
This simplifies to:
\[ h = \frac{x^2}{\frac{x}{2}} = \frac{x^2 \times 2}{x} = 2x \]

### Conclusion
Thus, the altitude of the triangle is:
\[ \boxed{2x} \text{ units} \]