If the area of a triangle with base x is equal to the area of a square with side x, then the altitude of the triangle is-

Question:If the area of a triangle with base \( x \) is equal to the area of a square with side \( x \), then the altitude of the triangle is:

1. $\( \frac{\pi}{2} \)$

2. $\( 2x \)$ (Correct Answer)

3. $\( 3x \)$

4. $\( x \)$

Explanation:

To find the correct answer, we need to compare the areas of a triangle and a square given certain parameters.

Step 1: Area of the Square:

A square with side length \( x \) has an area given by:

$\[ A_{\text{square}} = x^2 \]$

Step 2: Area of the Triangle

A triangle with base \( x \) and height \( h \) has an area given by:

$\[ A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times x \times h \]$

<h3>Step 3: Equating the Areas</h3>

According to the problem, the areas of the two shapes are equal:

$\[ \frac{1}{2} x h = x^2 \]$

Step 4: Solving for $\( h \)$

We can solve for the height \( h \) by isolating it on one side of the equation. First, cancel out \( x \) from both sides (assuming \( x \neq 0 \)):

$\[ \frac{1}{2} h = x \]$

Then multiply both sides by 2:

$\[ h = 2x \]$

Conclusion:

Thus, the altitude (or height) of the triangle is \( 2x \), making option 2 the correct answer.