Answer:
The scale factor is
27.5 feet / 22 feet = 1.25.
Explanation:
Whenever you are calculating factors, you are comparing two measurements. In this problem we compared a longer length to a shorter length pool. The length was changed to (27.5 feet) and youre comparing to the length it was originally (22 feet).
Ok so you know the two measurements being compared, but how come it’s 27.5/22 and not 22/27.5? Because the value got bigger.
In this problem you had a pool with long side of 22 ft. But then you made it longer to 27.5 ft. So it scales up,
It went from 100% its length to 125% its length. So the length is 125% / 100% = 1.25 times longer than it used to be.
Here’s another example:
How do you calculate your grade percentage on a test? You take the amount of points you earned and divide by the total possible points. Your grade percentage is a comparison of your score (Compare value) compared to a perfect score (reference value) .
So lets say your test had 22 total points. You get all the answers correct so you get 22/22 points which is 22/22*100 = 100%. Let’s say you get an extra bonus question correct so you end up with even more points and you get 27.5 points out of 22. By getting the bonus points you scaled up your score! Now your score is 27.5/22 * 100 = 125%. So you went from 100% to a 125%. Or from a scale factor of 1 to 1.25.
Whenever the value is getting bigger than it was, you’re going to have a compared percentage over 100%. If the value gets smaller, then you would get a compared percentage less than 100%. Similarly a factor scale is going to be over 1 if the compared value is getting bigger, and less than 1 if it’s getting smaller.
So you don’t need to use percentages, factors are the same they just look a little different.
27.5/22 = 125% / 100% = 1.25
In summary just do this division:
(compare value)/(reference value). The result is how big the top value is compared to the bottom value.
.
subject to the constraint 
. Note that 
and 
attain their extrema at the same values of 
, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
.
, which means the shortest distance must be 
.