Find the area of an equilateral triangle whose height is `sqrt(48)` cm . The following steps are involved in solving the above problem . Arrange them in sequential order .
`:. ` Area of the equilateral triangle `= (sqrt(3))/4 xx 64 = 16 sqrt(3) cm^(2)`
Let the side of the equilateral triangle be a cm .
` :. ` Height of the equilateral triangle `= (sqrt(3)a)/2 `
` :. ` Area of an equilateral triangle whose side is a cm = `(sqrt(3))/4 a^(2) = (sqrt(3))/4 xx (8)^(2) ( :' a = 8 cm)`
Given `(sqrt(3)a)/2 = sqrt(48) rArr a = 8 cm `

Options

A. BDCA
B. ABCD
C. BDAC
D. DBCA

Answer

To find the area of an equilateral triangle whose height is given as \( \sqrt{48} \) cm, we can follow these steps:

### Step 1: Relate the height to the side of the triangle
The height \( h \) of an equilateral triangle is related to its side \( a \) by the formula:
\[ h = \frac{\sqrt{3}}{2} a \]
Given that the height \( h = \sqrt{48} \) cm, we can set up the equation:
\[ \sqrt{48} = \frac{\sqrt{3}}{2} a \]

### Step 2: Solve for the side \( a \)
To find \( a \), we can rearrange the equation:
\[ a = \frac{2 \sqrt{48}}{\sqrt{3}} \]
Next, simplify \( \sqrt{48} \):
\[ \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \]
Substituting this back into the equation for \( a \):
\[ a = \frac{2 \times 4\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{\sqrt{3}} = 8 \text{ cm} \]

### Step 3: Calculate the area of the equilateral triangle
The area \( A \) of an equilateral triangle with side \( a \) is given by the formula:
\[ A = \frac{\sqrt{3}}{4} a^2 \]
Substituting \( a = 8 \) cm into the formula:
\[ A = \frac{\sqrt{3}}{4} \times (8)^2 = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3} \text{ cm}^2 \]

### Final Result
Thus, the area of the equilateral triangle is:
\[ \boxed{16\sqrt{3} \text{ cm}^2} \]