Accessible Ramp Compliance
A school is installing a wheelchair ramp at the main entrance. The door threshold is 27 inches above the sidewalk. The available straight run along the building wall is 25 feet. State code requires a ramp slope no steeper than 1:12, meaning 1 inch of rise for every 12 inches of horizontal run. The maintenance director proposes using the full 25 feet as the horizontal run. A parent points out that the handrail must follow the slanted surface of the ramp, so the surface length, not just the horizontal run, determines how much railing to order. The school can either lower the threshold to 24 inches or extend the run by 3 feet into the courtyard, but not both. Construction costs are similar, so the school will choose the option with the gentler slope.
1. Convert the proposed run to inches, compute the slope ratio as a ratio of rise to run, and decide whether the 25-foot design meets the 1:12 code.
Read the worked answer
Run = 25 × 12 = 300 in. Slope = rise/run = 27/300 = 0.09 = 9%, which as a ratio is 27:300 = 1:11.11. The code maximum is 1:12 ≈ 0.0833. Since 0.09 > 0.0833, the design is too steep and fails. The required run for 27 in of rise is 27 × 12 = 324 in = 27 ft, so the proposed run is 24 in short.
2. Evaluate both options and determine which has the gentler slope.
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Option 1, lower the threshold: rise 24 in, run 300 in; slope = 24/300 = 0.08 = 1:12.5, angle arctan(0.08) ≈ 4.57°. Option 2, extend the run: run = 336 in, rise 27 in; slope = 27/336 ≈ 0.08036 = 1:12.44, angle ≈ 4.60°. Both are gentler than 1:12 (0.0833). Option 1 has the smaller slope, so it is slightly gentler and is the chosen design.
3. For the chosen option, compute the slanted surface length to the nearest inch for ordering handrail.
Read the worked answer
For Option 1, surface length = square root of (24² + 300²) = square root of (576 + 90,000) = square root of 90,576 ≈ 300.96 in, so order 301 in of railing. If the school chose Option 2 instead, the length would be square root of (27² + 336²) = square root of 113,625 ≈ 337.08 in, or 337 in. The surface length is longer than the horizontal run because the ramp is the hypotenuse.