Triangle similarity

Find out if the triangles ABC and A'B'C' are similar, determine the similarity coefficient and write the similarity:
a = 40 mm, b = 48 mm, c = 32 mm
a´ = 60 mm, b´ = 50 mm, c´ = 40 mm

Final Answer:

k =  1.25

Step-by-step explanation:

$$\begin{gathered} a=40\text{mm} \\ b=48\text{mm} \\ c=32\text{mm} \\ {a}_2=60\text{mm} \\ {b}_2=50\text{mm} \\ {c}_2=40\text{mm} \\ b>a>c \\ {a}_2>b_2>c_2 \\ {k}_1=a_2/b=60/48=\frac{5}{4}=1\frac{1}{4}=1.25 \\ {k}_2=b_2/a=50/40=\frac{5}{4}=1\frac{1}{4}=1.25 \\ {k}_3=c_2/c=40/32=\frac{5}{4}=1\frac{1}{4}=1.25 \\ {k}_1=k_2=k_3 \\ k=k_1=1.25=\frac{5}{4}=1\frac{1}{4} \\ k\cdot ABC=B^{\prime }{A}^{\prime }{C}^{\prime } \end{gathered}$$

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