Chapter 9.6, Problem 20PSC

To determine

To prove: The only right-triangle is (3,4,5) right-triangle in which the sides are consecutive integer.

Explanation of Solution

Given information :

Lengths of sides of right angle as (3, 4, 5)

Formula used :

Pythagoras theorem

Proof :

Pythagoras theorem says that

  $\begin{array}{l}{\left(\text{Hypotenuse}\right)}^2={\left(\text{Perpendicular}\right)}^2+{\left(\text{Base}\right)}^2\\ \Rightarrow {\left(\text{5}\right)}^2={\left(3\right)}^2+{\left(\text{4}\right)}^2\end{array}$

Hence proved