If the side of a triangle are in the ratio 3:4:5, prove that it is right -angled triangle.

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Solution

Given the sides are in the ratio $3 : 4 : 5.$
Let $A B C$ be the given triangle.
Let the sides be $3 x, 4 x$ and hypotenuse be $5 x .$
According to Pythagoras theorem,
$A C^{2} = B C^{2} + A B^{2}$
$B C^{2} + A B^{2} = (3 x)^{2} + (4 x)^{2}$
$= 9 x^{2} + 16 x^{2}$ $= 25 x^{2}$
$A C^{2} = (5 x)^{2} = 25 x^{2}$
$A C^{2} = B C^{2} + A B^{2}$
Hence $A B C$ is a right angled triangle.

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