Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

A black trail and a gray trail cross a park as shown. Each trail divides a park in two regions of equal area. Which of the following must be true about the areas A, B, and C?  Let's consider the sides of the trails. D be the leftmost portion of the park and E be the rightmost portion. We know that the left area of the black trail has area D plus  B and the left of the gray trail has area A plus D plus C. These are both equal to half the area of the park and thus D plus B equals A plus D plus C giving us the relation that  B is A plus C.

Video Summary

The video explains how two trails, black and gray, divide a park into two regions of equal area. Using these divisions, it concludes that the area on the left of the black trail (D + B) is equal to the area on the left of the gray trail (A + D + C). This equality results in the relationship B = A + C.