To find the length of the perpendicular of the triangle, we can start by understanding the relationship between the base, perpendicular, and the area of a right-angled triangle. In a right-angled triangle, the area can be calculated using the formula: Area = 0.5 * base * perpendicular.
Given that the base of the triangle is 2x units and the area is 4x² + 4, we can set up the equation:
4x² + 4 = 0.5 * 2x * perpendicular
Now, we can simplify the equation:
4x² + 4 = x * perpendicular
4x² = x * perpendicular - 4
4x² = x(perpendicular - 4)
To find the length of the perpendicular, we need to isolate perpendicular in the equation:
perpendicular - 4 = 4x² / x
perpendicular - 4 = 4x
perpendicular = 4x + 4
Therefore, the length of the perpendicular of the triangle is 4x + 4 units.
