Question

Is the triangle with sides $25cm,5cm$ and $24cm$ a right triangle? Give a reason for your answer.

Answer 1

Defining right angle triangle :

A right angle is a triangle in which one angle is a right angle or two sides are perpendicular. A right-angle triangle satisfies the Pythagoras theorem.

Let us consider, $A=25cm,B=5cm,C=24cm$

applying the Pythagoras theorem,

$A^2=B^2+C^2$

Taking L.H.S.

$$\begin{gathered} A^2={25}^2 \\ \Rightarrow A^2=625 \end{gathered}$$

Taking R.H.S.

$$\begin{gathered} B^2+C^2={\left(5\right)}^2+{\left(24\right)}^2 \\ \Rightarrow B^2+C^2=25+576 \\ \Rightarrow B^2+C^2=601 \end{gathered}$$

Comparing L.H.S. and R.H.S.

$625\ne 601$

$\Rightarrow$L.H.S.$\ne$R.H.S.

The sides do not satisfy the property of the Pythagoras theorem.

Hence, the given triangle is not a right-angle triangle.