Chapter 10.1, Problem 17P

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

16 cm, 30 cm, 34 cm

To determine

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

Answer to Problem 17P

It is a right angled triangle.

Explanation of Solution

Given information:

The given lengths are:

  $16cm,30cm,34cm$

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:

  $\begin{array}{l}{\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2\\ {34}^2={30}^2+{16}^2\\ 1156=900+256\\ 1156=1156\end{array}$

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