Chapter 10.1, Problem 24P

Determine whether the given lengths can be side lengths of a right triangle. $\frac{1}{3}yd,\frac{1}{4}yd,\frac{1}{5}yd$

To determine

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

Answer to Problem 24P

It is not a right angled triangle.

Explanation of Solution

Given information:

The given lengths are:

  $\frac{1}{3}yd,\frac{1}{4}yd,\frac{1}{5}yd$

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:

  $\begin{array}{l}{\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2\\ {\left(\frac{1}{3}\right)}^2={\left(\frac{1}{4}\right)}^2+{\left(\frac{1}{5}\right)}^2\\ \frac{1}{9}=\frac{1}{16}+\frac{1}{25}\\ \frac{1}{9}=\frac{1}{16}+\frac{1}{25}\\ 0.1111\ne 0.1025\end{array}$

Since, the equation is not satisfied, it is not a right angled triangle.