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8. If the sides of a triangle are in the ratio 1: √2: 1, show that it is a right-angled triangle.​

8. If the sides of a triangle are in the ratio 1: √2: 1, show that it is a right-angled triangle.​

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
9 months ago
Dear Student

As we observe that the greatest side of the given triangle is √2.
In given right angled triangle,
saya=x,b=√2​x,c=xthen
Using Pythagoras theorem,
a^2+c^2=b^2
LHS=a^2+c^2=x^2+x^2=2x^2unit,
RHS=
=b^2=(2​x)^2=2x^2unit,
LHS=RHS
Hence,
If the sides of a triangle are in the ratio1:2​:1,
then it is a right-angled triangle.

Thanks

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