The triangle bounded by the lines y = 0, y = 2x and y = -0.5x + k

 The triangle bounded by the lines y = 0, y = 2x and y = -0.5x + k

The triangle bounded by the lines y = 0, y = 2x and y = -0.5x + k, with k positive, is equal to 80 square units. Find k.

Answer：A(0,0) , B(2k/5 , 4k/5) , C(2k ,0) : points of intersection of the 3 points of intersection of the 3 lines
(1/2) × (4k/5) × (2k) = 80 : area given
k = 10 : solve the above equation for k , k positive is a given condition.