If an ice rink is #sqrt(404)# across then what is its perimeter?
1 Answer
It could be
Explanation:
Since there is not enough information in the question, let us work with the following assumptions:

The ice rink is rectangular.

The length of each side is an integer.

The diagonal measurement of the ice rink is
#sqrt(404)# . 
The rectangle is as close as possible to being square given the above conditions.
By Pythagoras, we can tell that we need a pair of positive integers, the sum of whose squares is
Note that:
#14 = sqrt(196) < sqrt(404/2) = sqrt(202) < sqrt(225) = 15#
So one of the sides of the rectangle is
Trying each possible larger side from

#404  15^2 = 404225 = color(red)(cancel(color(black)(179)))# 
#404  16^2 = 404256 = color(red)(cancel(color(black)(148)))# 
#404  17^2 = 404289 = color(red)(cancel(color(black)(115)))# 
#404  18^2 = 404324 = color(red)(cancel(color(black)(80)))# 
#404  19^2 = 404361 = color(red)(cancel(color(black)(43)))# 
#404  20^2 = 404400 = 4 = 2^2#
So with the above assumptions, the ice rink is
Well there's an answer, but