Final answer:
The benefit of a perpendicular approach lies in optimizing certain factors such as maximizing area or minimizing the distance over 45-degree transections. This might mean more equitable and manageable partitions in case of area division, as well as the shortest path in a grid system.
Step-by-step explanation:
The benefit of a perpendicular approach compared to 45-degree transections is primarily in the area of optimization in different contexts, for instance in maximizing area or minimizing distance. Suppose you have a grid of streets where the avenues run north-south and the streets east-west, forming a grid pattern with 90-degree intersections. If you are at one corner and your destination is at the intersection diagonally across from you, the shortest path would involve two perpendicular paths (east then north, or north then east), which when added together form the hypotenuse of a right-angled triangle, which is the shortest distance between the two points following the grid. However, if the question refers to transecting an area, such as a field, for analysis or division purposes, utilizing a perpendicular or 90-degree approach as opposed to a 45-degree pattern could potentially lead to more equitable and manageable partitions. This is because a perpendicular transection results in rectangles or squares, which can be more easily calculated and managed when it comes to area and percentage divisions.