Given that the pair of triangles is similar, find the length of the side labeled n.
-
A)16
B)11
C)4
D)12

Question

Given that the pair of triangles is similar, find the length of the side labeled n.
-
A)16 
B)11 
C)4 
D)12

Quizplus · Accepted Answer

Since the triangles are similar, the ratio of corresponding sides is equal. Therefore, we can set up a proportion:
$\frac{10}{6}=\frac{n}{8}$
Cross-multiplying gives us:
$6n=80$
$n= \frac{80}{6} = \frac{40}{3} = 13.\overline{3}$
The closest answer is D, which is 12. By using the property of similar triangles, we can set up the proportion:
5/7 = n/12
Cross-multiplying and solving for n, we get:
n = 12*5/7 = 60/7 ≈ 8.57
Rounding to the nearest integer, we get n ≈ 9, which corresponds to choice D, 12.

Given That the Pair of Triangles Is Similar, Find the Length