The sides of certain triangles are given below. Determine which of them are right triangles.
(iii) $a\ =\ 1.6\ cm,\ b\ =\ 3.8\ cm$ and $c\ =\ 4\ cm$

Given:

The sides of a triangle are $a=1.6\ cm, b=3.8\ cm$, and $c=4\ cm$.

To do:

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

Solution:

$a=1.6\ cm$

$b=3.8\ cm$

$c=4\ cm$

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,

$(a)^2=(1.6\ cm)^2=2.56\ cm^2$

$(b)^2=(3.8\ cm)^2=14.44\ cm^2$

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

Here, $(a)^2+(b)^2=(2.56+14.44)\ cm^2=17\ cm^2$

$(a)^2+(b)^2≠(c)^2$

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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