Chapter SH, Problem 10.5.14EP

To determine

Whether the given measures can be the side of right triangle or not.

Answer to Problem 10.5.14EP

No

Explanation of Solution

Given:

The given sides are:

  $20,30,40$

Calculation:

The given measures will be the side of a right triangle if they fulfill the Pythagorean triplet formula, that is:

  $c^2=a^2+b^2$

The longest side is the hypotenuse, therefore,

  $\begin{array}{l}{c}^2=a^2+b^2\\ {\left(40\right)}^2={\left(20\right)}^2+{\left(30\right)}^2\\ 1600=400+900\\ 1600=1300\end{array}$

Hence, the given measures are not a Pythagorean triplet and therefore, are not the sides of right triangle.