Chapter 12, Problem 105CUR

To determine

To find: Whether the triangle with the given side lengths is a right angle.

Answer to Problem 105CUR

The triangle with the given side lengths $2,3,4$ is not a right angle.

Explanation of Solution

Given information: Given sides, $2,3,4$ .

Calculation: Since, For a right triangle the square of the hypotenuse is equal to the sum of the square of perpendicular and square of the base.

Let, Hypotenuse $=4$ , Perpendicular $=3$ , and Base $=2$

Therefore,

  $\begin{array}{c}{\text{Hypotenuse}}^2=4^2\\ =16\end{array}$

And

  $\begin{array}{c}{\text{Perpendicular}}^2+{\text{Base}}^2=3^2+2^2\\ =9+4\\ =13\end{array}$

Hence, The triangle with the given side lengths $2,3,4$ is not a right angle .