A line forms a triangle of area `54sqrt(3)s q u a r e` units with the coordinate axes. Find the equation of the line if the perpendicular drawn from the origin to the line makes an angle of `60^0` with the X-axis.

Explanation

To find the equation of the line that forms a triangle of area \(54\sqrt{3}\) square units with the coordinate axes, and for which the perpendicular drawn from the origin makes an angle of \(60^\circ\) with the x-axis, we can follow these steps:

### Step 1: Understand the Area of the Triangle
The area \(A\) of a triangle formed by a line with the coordinate axes can be expressed as:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Let the x-intercept be \(a\) and the y-intercept be \(b\). Then the area can be rewritten as:
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