Chapter 12, Problem 104CUR

To determine

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

Answer to Problem 104CUR

The triangle with the given side lengths $10,24,26$ is a right angle.

Explanation of Solution

Given information: Given sides, $10,24,26$ .

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 $=26$ , Perpendicular $=24$ , and Base $=10$

Therefore,

  $\begin{array}{c}{\text{Hypotenuse}}^2={26}^2\\ =676\end{array}$

And

  $\begin{array}{c}{\text{Perpendicular}}^2+{\text{Base}}^2={24}^2+{10}^2\\ =576+100\\ =676\end{array}$

Hence, The triangle with the given side lengths $10,24,26$ is a right angle .