Question

Tell whether the triangle with the given sides is a right triangle

Answer 1

The triangle is NOT a right triangle.

Explanation:

Given the side lengths: 14mm, 19mm, and 23mm.

To determine if they form a right triangle, check to see if they satisfy the Pythagorean Theorem:

`\begin{gathered} c^2=a^2+b^2 \\ \text{ where c is the longest side} \end{gathered}`
`\begin{gathered} c^2=23^2=529 \\ a^2+b^2=14^2+19^2=557 \\ c^2\cancel{=}a^2+b^2 \end{gathered}`
`\begin{gathered} c^2=23^2=529 \\ a^2+b^2=14^2+19^2=557 \\ c^2\cancel{=}a^2+b^2 \end{gathered}`

Since 529 is not equal to 557, the triangle is NOT a right triangle.