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.

$\left(i\right)a=5cm,b=3cm,c=4cm$

Answer 1

Step 1: Note the given data:

From the given triangle

The length of $a=5cm,$

The length of $b=3cm,$

The length of $c=4cm$

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, $a=5cm$ is the longest side.

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

L.H.S.

$$\begin{gathered} a^2=5^2 \\ =25 \end{gathered}$$

R.H.S.

$b^2+c^2=3^2+4^2$

$=9+16$

$=25$

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

Hence, the triangle is a right-angled triangle.