Question

1. triangle abc has sides ab = 8x, ac = 12, and bc = 15. triangle def has sides de = 24, df = 12, and ef = 15. what value of x makes the triangles congruent by sss?

a. 4
b. 5
c. 2
d. 3

Explanation:

Step1: Identify congruent sides

For SSS congruence, corresponding sides must be equal. So \( AB = DE \), \( AC = DF \), \( BC = EF \). Here, \( AC = 12 \), \( DF = 12 \) (matches), \( BC = 15 \), \( EF = 15 \) (matches), so \( AB = DE \).

Step2: Set up equation

\( AB = 8x \), \( DE = 24 \). So \( 8x = 24 \).

Step3: Solve for x

Divide both sides by 8: \( x=\frac{24}{8}=3 \)? Wait, no, wait. Wait, wait, maybe I mixed up. Wait, \( AB = 8x \), \( DE = 24 \). Wait, no, maybe \( AB \) corresponds to \( DE \)? Wait, no, let's check again. Triangle ABC: AB=8x, AC=12, BC=15. Triangle DEF: DE=24, DF=12, EF=15. So AC (12) corresponds to DF (12), BC (15) corresponds to EF (15), so AB (8x) must correspond to DE (24). So \( 8x = 24 \), so \( x = 24/8 = 3 \)? But wait, the options have d.3? Wait, but let's check again. Wait, maybe I made a mistake. Wait, no, 8x=24, x=3. But wait, the options: a.4, b.5, c.2, d.3. So x=3, which is option d? Wait, no, wait, 8x=24, x=3. So the answer should be 3.
Wait, no, wait, maybe I mixed up the sides. Wait, AB is 8x, DE is 24. So 8x=24, x=3. So the value of x is 3.

Answer:

d. 3