Chapter 8.6, Problem 53S

To determine

To find: the given possible lengths are the sides of a right triangle.

Explanation of Solution

Given information: the given possible lengths are the sides of a right triangle

  $60,80,100$ .

Formula used: The Pythagorean Theorem gives $a^2+b^2=c^2$ for a right triangle, where c is the hypotenuse and a and b are the smaller sides.

Proof: the given possible lengths are the sides of a right triangle.

  $60,80,100$

The Pythagorean Theorem gives $a^2+b^2=c^2$ for a right triangle, where c is the hypotenuse and a and b are the smaller sides.

Here $c=100$

  $\begin{array}{l}{a}^2+b^2=c^2\\ {60}^2+{80}^2={100}^2\\ 3600+6400=10000\\ 10000=10000\end{array}$

So, the given possible lengths are the sides of a right triangle.