
Construction When you climb a staircase, the flat part of a stair that you step on is called the tread of the stair. The riser is the vertical part of the stair. The slope of a staircase is the ratio of the length of the riser to the length of the tread. Because the design of a staircase may affect safety, most cities have building codes that give rules for the design of a staircase.
- The traditional design of a staircase calls for a 9-inch tread and an 8.25-inch riser. What is the slope of this staircase?
- A newer design for a staircase uses an 11-inch tread and a 7-inch riser. What is the slope of this staircase?
- An architect is designing a house with a staircase that is 8 ft high and 12 ft long. Is the architect using the traditional design in part a or the newer design in part b? Explain your answer.
- Staircases that have a slope between 0.5 and 0.7 are usually considered safer than those with a slope greater than 0.7. Design a safe staircase that goes from the first floor of a house to the second floor, which is 9 ft above the first floor.
- Measure the tread and riser for three staircases you encounter. Do these staircases match the traditional design in part a or the newer design in part b?

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