Question

What is the length of AB?

Answer 1

angle B'CA'= angle BCA..... (common angle)

angle B'A'C = angle BAC.....(corresponding angels)

therefore,

ΔCB'A' ~ ΔCBA. ......(by A-A test of similarity)

therefore,

B'A'/ BA. = CA'/ CA....(congruent sides of congruent triangles)

now, B'A' = 5, CA'= 6 , CA = 6 + 3 = 9

5 / BA. = 6 / 9

therefore, 5 / BA. = 2 / 3

`ba \: = (5 * 3)/(2 ) \\ = (15)/(2) \\ = 7.5`

Answer : AB = 7.5 units