If the sides of the rectangle are y and z, then the area of the shaded region will be the area of the rectangle minus the area of the unshaded triangle,

5x^2 = yz - 0.5*x*2x = yz - x^2

solve for the area of the rectangle, yz

yz = 6x^2

The answers represent potential sides of the rectangle, so we seek the answer whose product is 6x^2. Only answer A gives such a result.

Area of unshaded area is = (2x*x)/2 = x^2
Total area of rectangle = 5x^2 + x^2 = 6x^2

Out of given option, only A makes sure that area is 6 x^2. Hence A