Chapter 10.1, Problem 29P

Any set of three positive integers that satisfies the equation $a^2+b^2=c^2$ is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple.

70, 240, 250

To determine

To find whether the set of given numbers is not a Pythagorean triple.

Answer to Problem 29P

The set of numbers is a Pythagorean triple.

Explanation of Solution

Given information:

The given numbers are:

  $70,240,250$

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:

  $\begin{array}{l}{c}^2=a^2+b^2\\ {250}^2={240}^2+{70}^2\\ 62500=57600+4900\\ 62500=62500\end{array}$

Since, the equation is satisfied, the set of numbers is a Pythagorean triple.