The sides of certain triangles are given below. Determine which of them are right triangles.
(iv) $a\ =\ 8\ cm,\ b\ =\ 10\ cm$ and $c\ =\ 6\ cm$

Given:

The sides of a triangle are $a=8\ cm, b=10\ cm$, and $c=6\ cm$.

To do:

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

Solution:

$a=8\ cm$

$b=10\ cm$

$c=6\ cm$

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,

$(a)^2=(8\ cm)^2=64\ cm^2$

$(b)^2=(10\ cm)^2=100\ cm^2$

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

Here, $(a)^2+(c)^2=(64+36)\ cm^2=100\ cm^2$

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

Therefore, by the converse of Pythagoras theorem, the given sides are the sides of a right triangle. 

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Updated on: 10-Oct-2022

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