Question

If the sides of a triangle are 3 cm, 4 cm and 6 cm long, determine whether the triangle is a right-angled triangle.

Answer 1

SOLUTION :  

Let AB = 3 cm , BC = 4 cm , AC = 6 cm

Here, the larger side is AC = 6 cm

AC² = (6)² = 36

AB² = (3)² = 9

BC² = (4)² = 16

By Converse of Pythagoras theorem: In a triangle , if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the side is a right angle. (AC² = AB² + BC²)

Here,

AC² ≠ AB² + BC²

36 ≠ 9 + 16

36 ≠ 25

Hence, the triangle with the given sides is not a right angled triangle.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Given sides of the triangle are 3cm, 4cm, 6cm.

We know that in a right angles triangle the square of the largest side is equal to sum of squares of the smaller sides.

Here, the largest side is 6cm.

Now,

⇒ 3^2 + 4^2

⇒ 9 + 16

⇒ 25 ≠ 36.

Therefore, the given triangle is not a right angled triangle.

Hope it helps!