Final answer:
To find the area of the largest rectangle, set y to 0 and solve for x to find one vertex. Plug this x-coordinate into the equation y = 125 - (3/2)x to find the y-coordinate of the vertex. Multiply the length and height of the rectangle to find its area.
Step-by-step explanation:
To find the area of the largest rectangle, we need to find the coordinates of its vertices. The vertex opposite the origin lies on the graph of the line y = 125 - (3/2)x. Since one side of the rectangle is on the positive x-axis, we can set y to 0 and solve for x: 0 = 125 - (3/2)x. Solving this equation, we find that x = 83.333. Thus, the rectangle has a length of 83.333 units.
Since another side of the rectangle is on the positive y-axis, its length would be the y-coordinate of the vertex opposite the origin. Plugging x = 83.333 into the equation y = 125 - (3/2)x, we find that y = 28.334. Thus, the rectangle has a height of 28.334 units.
To find the area of the rectangle, we multiply its length by its height: Area = 83.333 * 28.334 = 2361.108 square units.