We should start by plotting the points on the x-y plane and get the co-ordinates of the three vertices of the triangle (PFA the image with the coordinates)
The height of the triangle is 3c and the base is 4c
Using the formula for Area of a triangle = (1/2) * Base * Height = (1/2) * 4c * 3c = 6c^2
Given that area = 54
=> 6c^2 = 54
=> c^2 = 54/6 = 9
=> c=3 (As c cannot be negative as it contributes to length of the triangle)
So, Answer will be A
Hope it helps!