Question 1120557
A park has a water channel with a semicircular cross section that has a radius of 13ft. The boats that are to be used in this water system have rectangular cross sections and are known to submerge 2 ft into the water.  If the water channel is to be filled with water 7.5ft deep, what is the maximum possible width of the boats?
===========
If you mean filled with water to a level of 7.5 feet:
The bottom of the boat would be 5.5 feet about the center of the channel and 7.5 feet from the top of the channel.
-----
With the Origin at the center of the top of the channel, the equation of the circle is {{{x^2 + y^2 = 13^2}}}
The bottom of the boat is on the line y = -7.5
{{{x^2 + (-7.5)^2 = 169}}}
x^2 = 112.75
x = ~10.62 feet
Width = ~21.24 feet maximum