Triangle Sides Perimeter

The triangle has a circumference of 35 cm. The first side is four centimeters larger than the second and, at the same time, 1 cm larger than the third side. Determine the sides of the triangle.

Final Answer:

a =  13.3333 cm
b =  9.3333 cm
c =  12.3333 cm

Step-by-step explanation:

$$\begin{gathered} a+b+c=35 \\ a=4+b \\ a=1+c \\ a+b+c=35 \\ a-b=4 \\ a-c=1 \\ Row2-Row1\to Row2 \\ -2b-c=-31 \\ Row3-Row1\to Row3 \\ -b-2c=-34 \\ Row3-\frac{-1}{-2}\cdot Row2\to Row3 \\ -1.5c=-18.5 \\ c=\frac{-18.5}{-1.5}=12.33333333 \\ b=\frac{-31+c}{-2}=\frac{-31+12.33333333}{-2}=9.33333333 \\ a=35-b-c=35-9.33333333-12.33333333=13.33333333 \\ a=\frac{40}{3}\doteq 13.333333 \\ b=\frac{28}{3}\doteq 9.333333 \\ c=\frac{37}{3}\doteq 12.333333 \end{gathered}$$

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