Chapter 6.3, Problem 44WE

To determine

The value of $\left(x\right)$ of the right angle triangle shown below using the Pythagoras Theorem.

  

Answer to Problem 44WE

The value of $\left(x\right)$ is $\sqrt{30}$ .

Explanation of Solution

Given information: The given right angle triangle has two sides $3\sqrt{5}\text{ and 5}\sqrt{3}$ respectively as shown.

  

Formula used: For a right angle triangle,

  $\left(\text{Hypotenuse}\right)=\sqrt{{\left(\text{Base}\right)}^2+{\left(\text{Perpendicular}\right)}^2}\mathrm{......}\left(1\right)$

Calculation: Evaluate $\left(x\right)$ with the help of formula (1),

  $\begin{array}{c}\left(5\sqrt{3}\right)=\sqrt{{\left(\text{3}\sqrt{5}\right)}^2+{\left(x\right)}^2}\\ 75=45+x^2\mathrm{......}\left(\text{Squared}\right)\\ \text{or, }{x}^2=30\\ x=\sqrt{30}\end{array}$