Triangle perimeter sides

The circumference of the triangle is 125 cm. The shortest side is 12 cm shorter than the longest side. The longest side is 7 cm longer than the middle side. How long is the middle side?

Final Answer:

b =  41 cm

Step-by-step explanation:

$$\begin{gathered} o=125\text{cm} \\ o=a+b+c \\ a=c-12 \\ c=7+b \\ 125=a+b+c \\ a=c-12 \\ c=7+b \\ a+b+c=125 \\ a-c=-12 \\ b-c=-7 \\ Row2-Row1\to Row2 \\ -b-2c=-137 \\ Row3+Row2\to Row3 \\ -3c=-144 \\ c=\frac{-144}{-3}=48 \\ b=\frac{-137+2c}{-1}=\frac{-137+2\cdot 48}{-1}=41=41\text{cm} \\ a=125-b-c=125-41-48=36 \\ a=36 \\ b=41 \\ c=48 \end{gathered}$$

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