Chapter 9.8, Problem 30E

To determine

Tofind:The triangle is right angled or not

Answer to Problem 30E

Right triangle

Explanation of Solution

Given information:

Sides of triangle- $a=2.5,b=6,c=6.5$

Concept Used:

Converse of Pythagoras theorem-

For a triangle with sides - $a,b,c$ if-

  $a^2+b^2=c^2$

Then the triangle is right angled.

Calculation:

  $\begin{array}{l}{a}^2+b^2=c^2\\ \Rightarrow {\left(2.5\right)}^2+{\left(6\right)}^2={\left(6.5\right)}^2\\ \Rightarrow 6.25+36=42.25\\ \Rightarrow 42.25=42.25\mathrm{...}\left(\text{true}\right)\end{array}$

Therefore the triangle is right angled.