Similar triangles

In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh.

Correct result:

f₂ =  3 cm
d₂ =  2.1 cm
e₂ =  4 cm

Solution:

$$\begin{gathered} f=21\text{ cm } \\ d=14.7\text{ cm } \\ e=28\text{ cm } \\ k={\displaystyle \frac{1}{7}}\doteq 0.1429 \\ k=f_2\mathrm{/}f \\ {f}_2=f\cdot k=21\cdot 0.1429=3\text{ cm} \end{gathered}$$

$d_2=d\cdot k=14.7\cdot 0.1429={\displaystyle \frac{21}{10}}={\displaystyle \frac{21}{10}}\text{ cm}=2.1\text{ cm}$

$e_2=e\cdot k=28\cdot 0.1429=4\text{ cm}$

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