Math Algebra 1, Eighth Grade

Question

In the diagram, △ABC∼△A′B′C′.

What are the lengths, in centimeters, of AC¯¯¯¯¯¯¯¯ and CB¯¯¯¯¯¯¯¯?

|AC|= __ cm

|CB|= __cm

Answer 1

They are similar so the ratios of the corresponding sides are the same:

x-1 = x+4

---- ------

2 3

cross multiply to solve for x:

3(x-1) = 2(x+4)

3x - 3= 2x + 8

x = 11

substitute value of x into expressions to find lengths

AC = x - 1 = 11 - 1 = 10

CB = x + 4 = 11 + 4 = 15