Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm² and if a: b: c = 12:7:18

Correct result:

a =  87.69 cm
b =  51.15 cm
c =  131.53 cm

Solution:

$$\begin{gathered} {s}_1={\displaystyle \frac{12+7+18}{2}}=18.5cm \\ {S}_1=\sqrt{s_1(s_1-12)(s_1-7)(s_1-18)}=26.295c{m}^2 \\ k=\sqrt{{\displaystyle \frac{1404}{S_1}}}=7.307 \\ a=12k=87.69\text{ cm} \end{gathered}$$

$b=7k=51.15\text{ cm}$

$c=18k=131.53\text{ cm}$

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