# Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.13 cm, 12 cm, 5 cm

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Given:

The sides of a triangle are $a=13\ cm, b=12\ cm$, and $c=5\ cm$.

To do:

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

Solution:

$a=13\ cm$

$b=12\ cm$

$c=5\ cm$

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,

$(a)^2=(13\ cm)^2=169\ cm^2$

$(b)^2=(12\ cm)^2=144\ cm^2$

$(c)^2=(5\ cm)^2=25\ cm^2$

Here, $(b)^2+(c)^2=(144+25)\ cm^2=169\ cm^2$

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

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

The length of the hypotenuse is $13\ cm$.

Updated on 10-Oct-2022 13:21:24