Question

If AB = 9, RS = 3, and SC = 5, find BC.
A) 5
B) 10
C) 13.5
D) 15

Answer 1

BC=15, so D

Explanation:

First, let's annotate. on line AB, write 9. RS, 3. SC, 5. These are the measurements of lines, not angles. We're trying to find the length of BC, the whole bottom side. Also, all of the little squares represent 90° angles, which means the triangles are also rational.

1. Lengths 3 and 9 are rational. 1:3.
2. Since they're rational, the triangles are a set of dilations.
3. Because of this, ALL the sides of the triangles are rational.
4. If all the sides are rational by 1:3, which they are, then we can just multiply SC by 3. By doing this, we get the length of BC.
5. Thus, the length of BC is 15.

I REALLY hope this helps. If not, I encourage you to watch videos on dilations/rational triangles.

Answer 2

D

Explanation:

Δ ABC and Δ RSC are similar triangles, thus the ratio of corresponding sides are equal, that is

`(BC)/(SC)` =
`(AB)/(RS)`, substitute values

`(BC)/(5)` =
`(9)/(3)` = 3 ( multiply both sides by 5 )

BC = 5 × 3 = 15 → D