Similarity of two triangles

The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0 if not, if yes, find and write the coefficient of a similarity)

Correct answer:

q =  1.3333

Step-by-step explanation:

$$\begin{gathered} k=6.3\text{ cm } \\ l=8.1\text{ cm } \\ m=11.1\text{ cm } \\ x=8.4\text{ cm } \\ y=10.8\text{ cm } \\ z=14.8\text{ cm } \\ k<l<m \\ x<y<z \\ {q}_1=x\mathrm{/}k=8.4\mathrm{/}6.3={\displaystyle \frac{4}{3}}=1\frac{1}{3}\doteq 1.3333 \\ {q}_2=y\mathrm{/}l=10.8\mathrm{/}8.1={\displaystyle \frac{4}{3}}=1\frac{1}{3}\doteq 1.3333 \\ {q}_3=z\mathrm{/}m=14.8\mathrm{/}11.1={\displaystyle \frac{4}{3}}=1\frac{1}{3}\doteq 1.3333 \\ {q}_1=q_2=q_3 \\ q=q_1=1.3333 \end{gathered}$$

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