The vertical reaction for the arch is A. $$\frac{{{\text{Wa}}}}{{2l}}$$ B. $$\frac{{{\text{W}}l}}{{\text{a}}}$$ C. $$\frac{{{\text{Wa}}}}{l}$$ D. $$\frac{{{\text{W}}{{\text{a}}^2}}}{{2l}}$$

The correct answer is $\frac{{{\text{Wa}}}}{{2l}}$.

The vertical reaction for the arch is the force that the supports exert on the arch to prevent it from falling over. It can be calculated by dividing the weight of the arch by the length of the arch.

The weight of the arch is equal to the product of the area of the arch and the density of the material. The area of the arch is equal to the product of the length of the arch and the width of the arch. The density of the material is a constant.

The length of the arch is the distance between the two supports.

Therefore, the vertical reaction for the arch is equal to:

$$\frac{{{\text{Wa}}}}{{2l}}$$

where:

• $W$ is the weight of the arch
• $a$ is the width of the arch
• $l$ is the length of the arch

The other options are incorrect because they do not take into account the width of the arch.