Question

In the following, $a,b,c$ denote the lengths of the sides of a triangle. Determine whether the triangle is a right-angled triangle.

$\left(iii\right)a=5cm,b=12cm,c=13cm$

Answer 1

Step 1: Note the given data

From the given triangle

The length of $a=5cm,$

The length of $b=12cm,$

The length of $c=13cm$.

Step 2: Check whether the triangle is a right-angled triangle or not

The converse of the Pythagoras theorem: In a triangle, if the square of one side is equal to the sum of the squares of the remaining two sides, then the triangle is a right-angled triangle.

We know that the hypotenuse is the longest side of the triangle.

Here, $c=13cm$ is the longest side.

If a triangle is a right-angled triangle, then $c^2=a^2+b^2$

L.H.S.

$$\begin{gathered} {13}^2 \\ =169 \end{gathered}$$

R.H.S.

$5^2+{12}^2$

$=25+144$

$=169$

Therefore, from the converse of the Pythagoras theorem, L.H.S. $=$R.H.S.

Hence, the triangle is a right-angled triangle.