Chapter 10.1, Problem 22P

Determine whether the given lengths can be side lengths of a right triangle.

18 mi, 81 mi, 82 mi

To determine

To find if the given lengths can be sides of a right angled triangle.

Answer to Problem 22P

It is not a right angled triangle.

Explanation of Solution

Given information:

The given lengths are:

  $18mi,81mi,82mi$

Formula used:

The following formula is used:

  ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2$

Calculation:

Take the largest side as the hypotenuse and substitute the values in the formula:

  $\begin{array}{l}{\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2\\ {82}^2={81}^2+{18}^2\\ 6724=6561+324\\ 6724\ne 6885\end{array}$

Since, the equation is not satisfied, it is not a right angled triangle.