Chapter 12, Problem 103CUR

To determine

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

Answer to Problem 103CUR

The triangle with the given side lengths $5,12,15$ is not a right angle.

Explanation of Solution

Given information: Given sides, $5,12,15$ .

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 $=15$ , Perpendicular $=12$ , and Base $=5$

Therefore,

  $\begin{array}{c}{\text{Hypotenuse}}^2={15}^2\\ =225\end{array}$

And

  $\begin{array}{c}{\text{Perpendicular}}^2+{\text{Base}}^2={12}^2+5^2\\ =144+25\\ =169\end{array}$

Hence, The triangle with the given side lengths $5,12,15$ is not a right angle .