Anew patio will be an irregular hexagon. the patio will have two long parallel sides and an area of 360 square feet. the area of a geometrically similar patio is 250 square feet, and it’s long parallel sides are 12.5 feet apart. what is the corresponding distance on the new patio

The length of the new patio will be evaluated as follows:
The area scale factor=(area of new patio)/(area of original patio)
=360/250
=36/25
but
Linear scale factor=√(area scale factor)
Linear scale factor=√(36/25)=6/5
thus the length of the patio will be:
length=(linear scale factor)*(length of the original patio)
=6/5×12.5=15 ft

Agreed i also had the same answer