Which one of the following is the equation for width of the step in a staircase, consider R being the rise, T being tread, D/2 being the depth and b is the width ?
- Ab = √(R²/T²)
- Bb = √(R² + T²)Correct
- Cb = √(R²·T²)
- Db = √(R² − T²)
Solution
Concept
Dimension of a step along its slope
Formula
b = √(R² + T²)
Step-by-step solution
1. The rise and the tread form the two sides of a right triangle. 2. The sloping dimension of the step is the hypotenuse: b = √(R² + T²).
Explanation
By Pythagoras the inclined length of a step is the square root of the sum of squares of the rise and the tread.
Why the other options are wrong
A ratio, a product or a difference of squares is not the length of the hypotenuse.
Shortcut
Hypotenuse = √(R² + T²).
Correct answer: B) b = √(R² + T²)