Triangle area

A triangle with a perimeter of 69 cm has one side three times shorter than the longest of them and the other 3 cm shorter than the longest of them. Find the area of the triangle.

Final Answer:

S =  142.1818 cm²

Step-by-step explanation:

$$\begin{gathered} o=69\text{cm} \\ a=c/3 \\ b=c-3 \\ o=a+b+c \\ o=c/3+(c-3)+c \\ 69=c/3+(c-3)+c \\ 7c=216 \\ c=\frac{216}{7}=30.85714286 \\ c=\frac{216}{7}\doteq 30.857143 \\ a=c/3=30.8571/3=\frac{72}{7}\doteq 10.2857\text{cm} \\ b=c-3=30.8571-3=\frac{195}{7}\doteq 27.8571\text{cm} \\ s=\frac{a+b+c}{2}=\frac{10.2857+27.8571+30.8571}{2}=\frac{69}{2}=34.5\text{cm} \\ S=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}=\sqrt{34.5\cdot (34.5-10.2857)\cdot (34.5-27.8571)\cdot (34.5-30.8571)}=142.1818{\text{cm}}^2 \end{gathered}$$

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