Right Triangle Perimeter

The side lengths of two triangles, sorted by size, are: 8 cm, 10 cm, 13 cm, 15 cm, 17 cm, and 19 cm. One of these two triangles is right-angled. Calculate the perimeter of this right triangle in centimeters

Final Answer:

o =  40 cm

Step-by-step explanation:

$$\begin{gathered} c_1=\sqrt{8^2+10^2}=2\sqrt{41}\text{cm}\doteq 12.8062\text{cm} \\ {c}_2=\sqrt{8^2+13^2}=\sqrt{233}\text{cm}\doteq 15.2643\text{cm} \\ {c}_3=\sqrt{8^2+15^2}=17\text{cm} \\ {c}_4=\sqrt{8^2+17^2}=\sqrt{353}\text{cm}\doteq 18.7883\text{cm} \\ {c}_5=\sqrt{10^2+13^2}=\sqrt{269}\text{cm}\doteq 16.4012\text{cm} \\ {c}_6=\sqrt{10^2+17^2}=\sqrt{389}\text{cm}\doteq 19.7231\text{cm} \\ {c}_7=\sqrt{13^2+15^2}=\sqrt{394}\text{cm}\doteq 19.8494\text{cm} \\ {c}_8=\sqrt{13^2+17^2}=\sqrt{458}\text{cm}\doteq 21.4009\text{cm} \\ {c}_9=\sqrt{15^2+17^2}=\sqrt{514}\text{cm}\doteq 22.6716\text{cm} \\ a=8\text{cm} \\ b=15\text{cm} \\ c=c_3=17\text{cm} \\ o=a+b+c=8+15+17=40\text{cm} \end{gathered}$$

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