# Thread: question on semi elliptical arch bridge

1. ## question on semi elliptical arch bridge

the arch bridge takes the shape of a circular arc. the portion of the arch bridge above the water has a span of 30m and a rise of 10m. a boat passes through the arch bridge. if the cross section of the boat is modeled by a rectangle with vertical sides, find correct to 2 decimal places the width of the boat which has the largest cross sectional area above water level. justify your answer.

2. You state semi-elliptical in the heading, but circular in the problem. It is

an ellipse with semi-major axis length 15 and semi-minor axis length 10.

The equation of said ellipse is $\frac{x^{2}}{15^{2}}+\frac{y^{2}}{10^{2}}=1$

The area of the rectangle, designating the boat, has area A=2xy

Solve the ellipse equation for y and sub into the area formula.

Differentiate w.r.t. x, set to 0 and solve for x. y will follow.

3. thanks (: