If the sides of a triangle are in the ratio 1 : √2 : 1, show that it is a right- angled triangle.
Answers
Answered by
47
sum of angles in a triangle=180.
Let the angles be x. So,
x+2x+x=180
4x=180
x=180/4=45
Therefore, x=45
2x=45*2=90 and
x=45
By the second angle it is proved that it is a right angled triangle.
Let the angles be x. So,
x+2x+x=180
4x=180
x=180/4=45
Therefore, x=45
2x=45*2=90 and
x=45
By the second angle it is proved that it is a right angled triangle.
Answered by
50
Let one side =x
According to ratio
1:1×√2:1
x:x√2:x
x=AB
x√2=BC
x=AC
BC^2=AB^2+AC^2
(x√2)^2=(x)^2+(x)^2
x^2×2=x^2+x^2
2x^2=2x^2
BC^2 is equal to AC^2+AB^2
hence given ratio is of right angled triangle.
According to ratio
1:1×√2:1
x:x√2:x
x=AB
x√2=BC
x=AC
BC^2=AB^2+AC^2
(x√2)^2=(x)^2+(x)^2
x^2×2=x^2+x^2
2x^2=2x^2
BC^2 is equal to AC^2+AB^2
hence given ratio is of right angled triangle.
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