An accessibility ramp for wheelchairs is to be made alongside the staircase. The guidelines given for the slope of the ramp is 1 cm vertical rise to 12 cm horizontal length. What should be the horizontal length of the ramp if the total height of the stairs is 18 cm?
Answer: Slope = 112, rise = 18 cm ⇒ horizontal length = 18 × 12 = 216 cm (2.16 m).
Step-by-step solution
Given: Slope = 112 (1 cm up for every 12 cm along); Total rise = 18 cm
To find: Horizontal length (run) of the ramp
To find: Horizontal length (run) of the ramp
Idea: Slope = riserun. Keep the slope 112 and put in the rise of 18 cm; then solve for the run.
- Let the horizontal length be L cm. Slope = riserun ⇒ 18L = 112.1 mark
- Cross-multiply: L = 18 × 12 = 216 cm (= 2.16 m).1 mark
The ramp must be 216 cm (2.16 m) long horizontally.
Check: 18216 = 112 ✓.
Answer to write in the exam
Slope = riserun ⇒ 18L = 112
L = 18 × 12
∴ Horizontal length = 216 cm
Common mistakes that cost marks
- Dividing 18 by 12 (1.5 cm), which mixes up rise and run.
- Taking the sloping length of the ramp instead of the horizontal length.
How this can come in the exam
Short answer (2 marks)
A ramp must have slope 115. If it climbs 0.6 m, how long is it horizontally?
Show answer
0.6L = 115 (1 mark) ⇒ L = 0.6 × 15 = 9 m (1 mark).Try one yourself
A path with slope 120 runs 300 m horizontally. How much does it rise?
Show answer
120 × 300 = 15 m.
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