Sides ratio

Calculate the circumference of a triangle with area 84 cm² if a:b:c = 10:17:21

Correct answer:

o =  48 cm

Step-by-step explanation:

$$\begin{gathered} a_1=10 \\ {b}_1=17 \\ {c}_1=21 \\ S=84 \\ {s}_1=(a_1+b_1+c_1)\mathrm{/}2=(10+17+21)\mathrm{/}2=24 \\ {S}_1=\sqrt{s_1\cdot (s_1-a_1)\cdot (s_1-b_1)\cdot (s_1-c_1)}=\sqrt{24\cdot (24-10)\cdot (24-17)\cdot (24-21)}=84 \\ k=\sqrt{S\mathrm{/}{S}_1}=\sqrt{84\mathrm{/}84}=1 \\ a=k\cdot a_1=1\cdot 10=10 \\ b=k\cdot b_1=1\cdot 17=17 \\ c=k\cdot c_1=1\cdot 21=21 \\ o=a+b+c=10+17+21=48\text{ cm} \end{gathered}$$

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