Final answer:
The student needs to build a ramp 48 feet in length to comply with the ADA slope recommendation of 1:12, meaning for every foot of height, 12 feet of ramp is required.
Step-by-step explanation:
The student's question involves using basic principles of geometry and algebra to solve a real-world problem related to construction and accessibility. To determine how many feet of ramp will be needed, one can use the ADA (Americans with Disabilities Act) recommendation for ramp slope, which is a 1:12 slope ratio. This means for every inch of height, 12 inches of ramp is required. Since the threshold of the egress door is 4 feet above the sidewalk, a ramp measuring 48 feet in length would be needed to comply with the 1:12 slope ratio.
To visualize this, you could imagine constructing a ramp as if you were placing one end of a board on top of a stack of books to create a slope. You would then measure certain distances from the bottom of the ramp, like 0.5 m, 1 m, etc., up to the full height that the ramp needs to reach.