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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
The sides of a triangle are $a=13\ cm, b=12\ cm$, and $c=5\ cm$.
We have to determine whether the triangle is a right-angled triangle.
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.
$(a)^2=(13\ cm)^2=169\ cm^2$
$(b)^2=(12\ cm)^2=144\ cm^2$
$(c)^2=(5\ cm)^2=25\ cm^2$
Here, $(b)^2+(c)^2=(144+25)\ cm^2=169\ cm^2$
Therefore, by the converse of Pythagoras theorem, the given sides are the sides of a right triangle.
The length of the hypotenuse is $13\ cm$.
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