Question

A, B, and C are collinear points, where B is between A and C. Find x if AB = x, BC = x + 6, and AC = 24. Then find the measures of AB and BC by substituting x back into the equation.

Answer 1

AB = 9, BC = 15

Explanation:

Since, A, B, and C are collinear points, where B is between A and C. i. e. A - B - C

`\therefore AC = AB + BC\\</p><p>\therefore 24 = x + x + 6\\</p><p>\therefore 24 = 2x + 6\\</p><p>\therefore 24 - 6 = 2x \\</p><p>\therefore 18 = 2x \\</p><p> \therefore \: (18)/(2) = x \\ \therefore \: x = 9`

`\therefore AC = AB + BC\\</p><p>\therefore 24 = x + x + 6\\</p><p>\therefore 24 = 2x + 6\\</p><p>\therefore 24 - 6 = 2x \\</p><p>\therefore 18 = 2x \\</p><p> \therefore \: (18)/(2) = x \\ \therefore \: x = 9 \\ \because \: AB = x \\ \huge \red{ \therefore AB = 9} \\ \\ \because \:BC = x + 6 \\ \therefore \: BC = 9 + 6 \\ \huge \purple{ \therefore \: BC = 15}`