Triangle - perimeter

The perimeter of the triangle is 110 cm. Side a is 6 cm longer than side b and 8 cm shorter than side c. Determine the lengths of the sides of the triangle.

Final Answer:

a =  38 cm
b =  32 cm
c =  40 cm

Step-by-step explanation:

$$\begin{gathered} o=110\text{cm} \\ a=6+b \\ b=c-8 \\ a+b+c=o \\ a+(a-6)+(b+8)=o \\ a+(a-6)+((a-6)+8)=o \\ a+(a-6)+((a-6)+8)=110 \\ 3a=114 \\ a=\frac{114}{3}=38 \\ a=38=38\text{cm} \end{gathered}$$

$b=a-6=38-6=32\text{cm}$

$$\begin{gathered} c=b+8=32+8=40=40\text{cm} \\ \text{ Verifying Solution: } \\ {o}_2=a+b+c=38+32+40=110\text{cm} \end{gathered}$$

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