Answer: The fourth set of sides
Step-by-step explanation:
For a set of side lengths to form a right triangle, they have to satisfy the Pythagorean theory [tex](a^{2} +b^{2} =c^{2} )[/tex]
First set of sides
a = 7.5 b = 18 c = 21.5
[tex]a^{2} +b^{2} =c^{2}\\7.5^{2} +18^{2} =21.5^{2} \\56.25 + 324 = 462.25\\380.25 \neq 462.25[/tex]
Second set of sides
a = 7.5 b = 19.5 c = 21.5
[tex]a^{2} +b^{2} =c^{2} \\7.5^{2} +19.5^{2} =21.5^{2} \\56.25 + 380.25 = 462.25\\436.5 \neq 462.25[/tex]
Third set of sides
a = 18 b = 19.25 c = 21.5
[tex]a^{2} +b^{2} =c^{2} \\18^{2} +19.5^{2} =21.5^{2} \\324 + 380.25 = 462.25\\704.25 \neq 462.25[/tex]
Fourth set of sides
a = 7.5 b = 18 c = 19.5
[tex]a^{2} +b^{2} =c^{2} \\7.5^{2} +18^{2} =19.5^{2} \\56.25 + 324 = 380.25\\380.25 = 380.25[/tex]
I hope that helped!
