Question

11/17/25, 12:35 am finding the missing side length given two similar triangles practice | geometry pr
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answers:
a. 4 in
b. 2 in
c. 1 in
d. 3 in

Explanation:

Step1: Identify corresponding sides

In similar triangles, corresponding sides are proportional. Let's assume the sides of Triangle 1 are \( 12 \) in, \( 10 \) in, \( 8 \) in and Triangle 2 has sides \( 6 \) in, \( 5 \) in, and the missing side (let's call it \( x \)). The ratio of the sides of Triangle 1 to Triangle 2 should be consistent. The ratio of \( 12 \) in (Triangle 1) to \( 6 \) in (Triangle 2) is \( \frac{12}{6}=2 \), and the ratio of \( 10 \) in (Triangle 1) to \( 5 \) in (Triangle 2) is \( \frac{10}{5}=2 \). So the ratio of similarity is \( 2 \).

Step2: Find the missing side

For the side of length \( 8 \) in in Triangle 1, the corresponding side in Triangle 2 (the missing side \( x \)) should satisfy \( \frac{8}{x}=2 \). Solving for \( x \), we get \( x = \frac{8}{2}=4 \)? Wait, no, wait. Wait, maybe I mixed up the correspondence. Wait, Triangle 1 has sides 12, 10, 8. Triangle 2 has 6, 5, and the other side. Wait, 12 corresponds to 6 (ratio 2), 10 corresponds to 5 (ratio 2), so 8 should correspond to the missing side with ratio 2? Wait, no, maybe the missing side is in Triangle 1? Wait, no, looking at the diagram, Triangle 1 has a side labeled with a missing part? Wait, no, the answer choices are for a missing side. Wait, maybe the sides: Triangle 1: AC = 12, CR = 10, AR = 8. Triangle 2: KE = 6, KY = 5, EY =? Wait, no, maybe the missing side is in Triangle 2? Wait, no, the answer choices are A.4, B.2, C.1, D.3. Wait, maybe I made a mistake. Wait, let's re - evaluate. Let's list the sides:

Triangle 1: Let's say sides are \( a = 12 \), \( b = 10 \), \( c = 8 \)

Triangle 2: sides are \( a'=6 \), \( b' = 5 \), \( c'=? \)

Since \( \frac{a}{a'}=\frac{12}{6}=2 \), \( \frac{b}{b'}=\frac{10}{5}=2 \), so the ratio of Triangle 1 to Triangle 2 is 2:1. So the side \( c = 8 \) in Triangle 1 corresponds to \( c' \) in Triangle 2, so \( \frac{c}{c'}=2 \), so \( c'=\frac{c}{2}=\frac{8}{2}=4 \)? But the answer choices have 4 as option A. Wait, but let's check again. Wait, maybe the missing side is in Triangle 1? No, the answer choices are for the missing side. Wait, maybe I got the correspondence wrong. Wait, maybe the sides of Triangle 2 are 6, 5, and the other side, and Triangle 1 has 12, 10, 8. So the ratio of Triangle 2 to Triangle 1 is \( \frac{6}{12}=\frac{1}{2} \), \( \frac{5}{10}=\frac{1}{2} \), so the side of length 8 in Triangle 1, the corresponding side in Triangle 2 is \( 8\times\frac{1}{2}=4 \)? Wait, but the answer choice A is 4. Wait, but let's check the answer choices. The answer choices are A.4, B.2, C.1, D.3. So according to this, the missing side is 4? But wait, maybe I messed up the diagram. Wait, looking at the diagram, Triangle 1 has a side with a missing label? Wait, no, the problem is "Finding the Missing Side Length Given Two Similar Triangles". So the two triangles are similar, so their sides are proportional. Let's assume that the sides of Triangle 1 are 12, 10, 8 and Triangle 2 are 6, 5, and x. Then \( \frac{12}{6}=\frac{10}{5}=\frac{8}{x} \). \( \frac{12}{6}=2 \), so \( \frac{8}{x}=2 \), so \( x = 4 \). So the missing side is 4 in.

Answer:

A. 4 in