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.

$\left(v\right)a=7cm,b=12cm,c=6cm$

Answer 1

Step 1: Note the given data

From the given triangle

The length of $a=7cm,$

The length of $b=12cm,$

The length of $c=6cm$.

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, $b=12cm$ is the longest side.

If a triangle is a right-angled triangle, then

$b^2=a^2+c^2$

L.H.S.

$$\begin{gathered} {12}^2 \\ =144 \end{gathered}$$

R.H.S.

$7^2+6^2$

$=49+36$

$=85$

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

Hence, the triangle is not a right-angled triangle.