Similarity coefficient

Given triangle ABC with sides a = 12 cm b = 9 cm c = 7 cm and triangle DEF with sides d = 8.4 cm, e = 6.3 cm f = 4.9 cm Find out if triangles ABC and DEF are similar if so, write the similarity coefficient and according to which sentence they are similar

Correct answer:

k =  1.4286

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm} \\ b=9\text{cm} \\ c=7\text{cm} \\ d=8.4\text{cm} \\ e=6.3\text{cm} \\ f=4.9\text{cm} \\ a>b>c \\ d>e>f \\ {k}_1=a/d=12/8.4=\frac{10}{7}=1\frac{3}{7}\doteq 1.4286 \\ {k}_2=b/e=9/6.3=\frac{10}{7}=1\frac{3}{7}\doteq 1.4286 \\ {k}_3=c/f=7/4.9=\frac{10}{7}=1\frac{3}{7}\doteq 1.4286 \\ {k}_1=k_2=k_3 \\ k=k_1=1.4286 \end{gathered}$$

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