The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.
How to calculate the scale factor?
Suppose the initial measurement of a figure was x units.
And let the figure is scaled and new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.
Then we have:
Thus, scale factor is the ratio of the new measurement to the old measurement.
For this case, we're specified that:
Dimensions of the original pool = 24 feet wide by 36 feet long
The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).
So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:
Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:
Scaled length = s times original length
Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.
Learn more about scale factors here :