Grade 12Analytical Geometry
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.
1 Answer
Harshit Singh
Dear Student
As we observe that the greatest side of the given triangle is √2.
In given right angled triangle,
saya=x,b=√2x,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=(2x)^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
As we observe that the greatest side of the given triangle is √2.
In given right angled triangle,
saya=x,b=√2x,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=(2x)^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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