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

Given:

The sides of a triangle are $3\ cm, 4\ cm$, and $6\ cm$ long.

To do:

We have to determine whether the triangle is a right-angled triangle.

Solution:

Let the sides of the triangle be,

$AB=3\ cm$

$BC=4\ cm$

$CA=6\ cm$

We know that,

If the square of the hypotenuse is equal to the sum of the squares of the other two sides, then the triangle is a right-angled triangle. 

Therefore,

$(AB)^2=(3\ cm)^2=9\ cm^2$

$(BC)^2=(4\ cm)^2=16\ cm^2$

$(CA)^2=(6\ cm)^2=36\ cm^2$

Here, $(AB)^2+(BC)^2=(9+16)\ cm^2=25\ cm^2$

$(AB)^2+(BC)^2≠ (CA)^2$

Therefore, by the converse of Pythagoras theorem, the given sides cannot be the sides of a right triangle.

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Updated on: 10-Oct-2022

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