Question

Triangle A′B′C′ is a dilation of △ABC. What is AB?

Two triangles ABC and A'B'C' where A'B'C' is the smaller triangle. One of the sides of ABC is 15 while two of the sides of A'B'C' are 6, and 10.

A. 4
B. 5
C. 9
D. 16

Answer 1

C. 9

Explanation:

From the picture attached, you can see ΔA'B'C' is a dilation of ΔABC which means image ΔA'B'C' is similar to ΔABC.

By the property of similarity corresponding sides of both the triangles will be proportional.

`(AB)/(A^(')B^(') ) =(BC)/(B^(') C^(') ) =(AC)/(A^(') C^(') )`

`(AB)/(6) =(15)/(10)`

`AB = (6 * 15)/(10)`

`AB = (90)/(10)`

AB = 9 units

Therefore, the length of AB is 9 units.