Chapter 10.1, Problem 23P

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

2.0 km, 2.1 km, 2.9 km

To determine

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

Answer to Problem 23P

It is a right angled triangle.

Explanation of Solution

Given information:

The given lengths are:

  $2.0km,2.1km,2.9km$

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:

  $\begin{array}{l}{\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2\\ {2.9}^2={2.1}^2+{2.0}^2\\ 8.41=4.41+4.00\\ 8.41=8.41\end{array}$

Since, the equation is satisfied, it is a right angled triangle.