Grades 11-12 Video Solutions 2026-2026_11-12

Video Transcription

Video Summary

The problem uses the rule that when a tree branch splits, the total cross-sectional area stays the same. The diameters at points A, B, and C are 1 cm, 4 cm, and 8 cm, so their areas are proportional to \(1^2\), \(4^2\), and \(8^2\). Adding these gives the area of branch D. Since area is proportional to the square of the diameter, \(x^2 = 1^2 + 4^2 + 8^2 = 81\), so \(x = 9\). Therefore, the diameter at D is 9 cm, which is choice A.

Keywords

tree branch splitting

cross-sectional area

diameter proportionality

Pythagorean area sum

branch diameter calculation