The perimeter

The perimeter of the triangle is 24, and the sides are integers and form an arithmetic sequence. Specify the side sizes of this triangle.

Final Answer:

a₁ =  5
b₁ =  8
c₁ =  11
a₂ =  6
b₂ =  8
c₂ =  10
a₃ =  7
b₃ =  8
c₃ =  9

Step-by-step explanation:

$$\begin{gathered} a+(a+x)+(a+2x)=24 \\ 3a+3x=24 \\ a+x=8 \\ {a}_1=5;x_1=3 \\ {a}_2=6;x_2=2 \\ {a}_3=7;x_3=1 \end{gathered}$$

$b_1=a_1+x_1=5+3=8$

$c_1=b_1+x_1=8+3=11$

$b_2=a_2+x_2=6+2=8$

$c_2=b_2+x_2=8+2=10$

$b_3=a_3+x_3=7+1=8$

$c_3=b_3+x_3=8+1=9$

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