An arch is in the from of a parabola with its axis vertical. The arch is 12 m high and 6 m wide at the base. How wide is it 6 m from the vertex of the parabola ?

Explanation

From the figure, AB is base and height is 12 m.
Consider parabola `x^(2)=4ay`.
From the figure, point (3,12) lies on the parabola.
`:." "9=4xxaxx12`
`:." "4a=(3)/(4)`

Therefore, equation of parabola is `x^(2)=(3)/(4)y`
When `y=6,x^(2)=(9)/(2)`.
`:.` Width `2xx(3)/(sqrt(2))=3sqrt(2)m`