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 answer:

f₂ =  3 cm
d₂ =  2.1 cm
e₂ =  4 cm

Step-by-step explanation:

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

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

$e_2=e\cdot k=28\cdot \frac{1}{7}=\frac{28\cdot 1}{7}=\frac{28}{7}=4\text{cm}$

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