If T and R are the tread and rise of a stair which carries a load w per square metre on slope, the corresponding load per square metre of the horizontal area, is A. $$\frac{{{\text{w}}\left( {{\text{R}} + {\text{T}}} \right)}}{{\text{T}}}$$ B. $$\frac{{{\text{w}}\sqrt {{{\text{R}}^2} + {{\text{T}}^2}} }}{{\text{T}}}$$ C. $$\frac{{{\text{w}}\sqrt {{\text{R}} + {\text{T}}} }}{{\text{T}}}$$ D. $${\text{w}}\frac{{\text{R}}}{{\text{T}}}$$

The correct answer is $\boxed{\frac{{{\text{w}}\sqrt {{{\text{R}}^2} + {{\text{T}}^2}} }}{{\text{T}}}}$.

The load per square metre of the horizontal area is the load per square metre on the slope divided by the cosine of the angle of the slope. The cosine of the angle of the slope is equal to the ratio of the horizontal distance to the vertical distance. In this case, the horizontal distance is the tread, $T$, and the vertical distance is the rise, $R$. Therefore, the cosine of the angle of the slope is $\frac{T}{R}$.

The load per square metre on the slope is $w$. Therefore, the load per square metre of the horizontal area is

$$\frac{{{\text{w}}\sqrt {{{\text{R}}^2} + {{\text{T}}^2}} }}{{\text{T}}}$$

Option A is incorrect because it does not divide by the cosine of the angle of the slope. Option B is incorrect because it does not take into account the fact that the load is not evenly distributed over the horizontal area. Option C is incorrect because it does not take into account the fact that the load is not evenly distributed over the horizontal area. Option D is incorrect because it does not divide by the cosine of the angle of the slope.