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

Options

A. ` (b)/(2)`
B. ` 2b `
C. b
D. 4b

Answer

To solve the problem, we need to find the altitude (height) of a triangle when the area of a square with side 'b' is equal to the area of that triangle with base 'b'.

### Step-by-Step Solution:

1. **Calculate the Area of the Square:**
The area of a square is given by the formula:
\[ \text{Area of Square} = \text{side}^2 = b^2 \]

2. **Calculate the Area of the Triangle:**
The area of a triangle is given by the formula:
\[ \text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times b \times h \]
where \( h \) is the height (altitude) of the triangle.

3. **Set the Areas Equal:**
Since the area of the square is equal to the area of the triangle, we can set the two area expressions equal to each other:
\[ b^2 = \frac{1}{2} \times b \times h \]

4. **Rearrange the Equation to Solve for Height (h):**
To isolate \( h \), we can multiply both sides of the equation by 2 to eliminate the fraction:
\[ 2b^2 = b \times h \]
Next, divide both sides by \( b \) (assuming \( b \neq 0 \)):
\[ h = \frac{2b^2}{b} = 2b \]

5. **Conclusion:**
Therefore, the altitude (height) of the triangle is:
\[ h = 2b \]