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)

Result

q =  1.333

Solution:

k=6.3 cm l=8.1 cm m=11.1 cm  x=8.4 cm y=10.8 cm z=14.8 cm  k<l<m x<y<z q1=x/k=8.4/6.3431.3333 q2=y/l=10.8/8.1431.3333 q3=z/m=14.8/11.1431.3333  q1=q2=q3  q=q1=1.3333431.33331.333k=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/k=8.4/6.3 \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \ \\ q_{2}=y/l=10.8/8.1 \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \ \\ q_{3}=z/m=14.8/11.1 \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \ \\ \ \\ q_{1}=q_{2}=q_{3} \ \\ \ \\ q=q_{1}=1.3333 \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \doteq 1.333



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