Sides od triangle

Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.

Correct answer:

a =  3 cm
b =  3.75 cm
c =  5.25 cm

Step-by-step explanation:

$$\begin{gathered} a_1=4 \\ {b}_1=5 \\ {c}_1=7 \\ {o}_1=a_1+b_1+c_1=4+5+7=16 \\ {o}_2=12 \\ k=o_2\mathrm{/}{o}_1=12\mathrm{/}16={\displaystyle \frac{3}{4}}=0.75 \\ a=a_1\cdot k=4\cdot 0.75=3\text{ cm} \end{gathered}$$

$b=b_1\cdot k=5\cdot 0.75={\displaystyle \frac{15}{4}}={\displaystyle \frac{15}{4}}\text{ cm}=3.75\text{ cm}$

$c=c_1\cdot k=7\cdot 0.75={\displaystyle \frac{21}{4}}={\displaystyle \frac{21}{4}}\text{ cm}=5.25\text{ cm}$

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