Grades 9-10 Video Solutions 2014-Grades 9-10 Video Solutions 2014 problem3

Grades 9-10 Video Solutions 2014 problem3

Video Transcription

Video Summary

In comparing the lengths of curves A, B, and C, the speaker calculates their lengths to determine the correct inequality. Curve A has a total length of 16 units from 8 segments, each 2 units. Curve B consists of 4 segments (8 units) plus a circle of radius 1, resulting in approximately 14.18 units. Curve C includes 4 segments and diagonals forming right triangles (8 units plus 4√2). Comparing parts of each curve, it’s established that \(2\pi\) (from Curve B) is greater than 4√2 (from Curve C). Therefore, the order is: A > B > C, making answer E correct.

Keywords

curve lengths

inequality

calculation

segments

geometry