Question

5. Given the following lengths, determine if the shape is a RIGHT triangle: 14, 16, 18 (2 points: 1 point for the correct answer, 1 point for showing your work) Your answer

Answer 1

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,

`\text{ a + b }>\text{ c ; b+ c }>\text{ a ; a + c }>b`

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,

`\begin{gathered} \text{ c}^2=a^2+b^2 \\ 18^2=14^2+16^2 \\ 324\text{ = }196\text{ + }257 \\ 324\text{ }\\e\text{ 457} \end{gathered}`

Therefore, checking the relationships of the given the following lengths, the figure is not a right tiangle.