An equilateral ` Delta ` having side length 6 cms is divided into smaller equilateral ` Delta ` of 2 cms side length each . Find the maximum possible no . Of such `Delta ` s that can be created out of the bigger ` Delta `

Options

A. `(1)/(2)`
B. 7
C. 6
D. 9

Answer

To solve the problem of finding the maximum number of smaller equilateral triangles that can be created from a larger equilateral triangle, we will follow these steps:

### Step 1: Calculate the area of the larger equilateral triangle.
The formula for the area \( A \) of an equilateral triangle with side length \( s \) is given by:

\[ A = \frac{\sqrt{3}}{4} s^2 \]

For the larger triangle with a side length of 6 cm:

\[ A_{\text{large}} = \frac{\sqrt{3}}{4} \times 6^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3} \text{ cm}^2 \]

### Step 2: Calculate the area of the smaller equilateral triangle.
Using the same formula for the smaller triangle with a side length of 2 cm:

\[ A_{\text{small}} = \frac{\sqrt{3}}{4} \times 2^2 = \frac{\sqrt{3}}{4} \times 4 = \sqrt{3} \text{ cm}^2 \]

### Step 3: Determine the number of smaller triangles that can fit into the larger triangle.
To find the maximum number of smaller triangles that can be formed from the larger triangle, we divide the area of the larger triangle by the area of the smaller triangle:

\[ \text{Number of smaller triangles} = \frac{A_{\text{large}}}{A_{\text{small}}} = \frac{9\sqrt{3}}{\sqrt{3}} = 9 \]

### Conclusion:
The maximum possible number of smaller equilateral triangles that can be created from the larger triangle is **9**.

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