Question

A new 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

Answer 1

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