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.
$13\, cm, 12\, cm, 5\, cm$
$13\, cm, 12\, cm, 5\, cm$
(A) Given that the sides are $13\, cm, 12\, cm,$ and $5\, cm$.
Squaring the lengths of these sides,we obtain $169, 144,$ and $25$.
Clearly,$144 + 25 = 169$.
Or,$12^2 + 5^2 = 13^2$.
The sides of the given triangle satisfy the Pythagoras theorem.
Therefore,it is a right triangle.
We know that the longest side of a right triangle is the hypotenuse.
Therefore,the length of the hypotenuse of this triangle is $13\, cm$.
Squaring the lengths of these sides,we obtain $169, 144,$ and $25$.
Clearly,$144 + 25 = 169$.
Or,$12^2 + 5^2 = 13^2$.
The sides of the given triangle satisfy the Pythagoras theorem.
Therefore,it is a right triangle.
We know that the longest side of a right triangle is the hypotenuse.
Therefore,the length of the hypotenuse of this triangle is $13\, cm$.
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