Question

What must be the length of

in order for to be similar to ?

Triangle J-K-L with side J-K as 12, K-L as 6, and J-L as 14. Triangle P-Q-R with side P-R as 21 and Q-R as 9.

A.
8

B.
15

C.
18

D.
19

Answer 1

B. 15

In order for two triangles to be similar, the ratio of corresponding sides must be the same.

So, in this case, we need to find the length of side Q-R in order for the triangles to be similar.

Ratio of corresponding sides in triangle J-K-L to triangle P-Q-R is:
J-K / P-R = 12 / 21 = 4 / 7
K-L / Q-R = 6 / 9 = 2 / 3
J-L / P-R = 14 / 21 = 2 / 3

For the two triangles to be similar, the ratio of J-K to P-R must be equal to the ratio of K-L to Q-R and J-L to P-R.

Thus, we can set up a proportion:
12 / 21 = 6 / x
12x = 126
x = 10.5

Therefore, the length of side Q-R must be 10.5 for the triangles to be similar.