Triangle Side Lengths

The triangle has side lengths expressed in whole centimeters. One of them measures 8 cm, and the sum of the remaining two sizes is 32 cm. Determine the lengths of the remaining sides. Find all solutions.

Final Answer:

b₁ =  13 cm
c₁ =  19 cm
b₂ =  14 cm
c₂ =  18 cm
b₃ =  15 cm
c₃ =  17 cm
b₄ =  16 cm
c₄ =  16 cm

Step-by-step explanation:

$$\begin{gathered} a=8\text{cm} \\ b+c=32\text{cm} \\ b>0;c>0;b<a+c;c<a+b \\ b>0;c>0;b<8+c;c<8+b;b+c=32 \\ 12<b<20 \\ c=32-b \\ c>b \\ {b}_1=13=13\text{cm} \end{gathered}$$

$c_1=32-b_1=32-13=19\text{cm}$

$b_2=14=14\text{cm}$

$c_2=32-b_2=32-14=18\text{cm}$

$b_3=15=15\text{cm}$

$c_3=32-b_3=32-15=17\text{cm}$

$b_4=16=16\text{cm}$

$c_4=32-b_4=32-16=16\text{cm}$

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