To be able to determine if the figure is a right triangle.
The given length must satifies the given conditions,
a.) The sum of the two sides must always be lesser than the other side. We get,
[tex]\text{ a + b }>\text{ c ; b+ c }>\text{ a ; a + c }>b[/tex]
Given: a = 14 ; b = 16 ; c = 18
Let's check,
a + b > c ; 14 + 16 > 18 = 30 > 18 Satisfies the criteria
b + c > a ; 16 + 18 > 14 = 34 > 14 Satisfies the criteria
a + c > b ; 14 + 18 > 16 = 32 > 16 Satisfies the criteria
b.) The square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean Theorem). We get,
[tex]\begin{gathered} \text{ c}^2=a^2+b^2 \\ 18^2=14^2+16^2 \\ 324\text{ = }196\text{ + }257 \\ 324\text{ }\ne\text{ 457} \end{gathered}[/tex]
Therefore, checking the relationships of the given the following lengths, the figure is not a right tiangle.
