If m-n , m , m+n are the lengths of the sides of an obtuse angled triangle , then n lies in

Question

Question : x, y, and z are the sides of a triangle. If z is the largest side and x²+ y² > z², then the triangle is a:
Option 1: Isosceles right angled triangle
Option 2: Acute angled triangle
Option 3: Obtuse angled triangle
Option 4: Right angled triangle

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Answer 1

Hello Aspirant...

Δ is obtused

greatest side will be m+n.

Smallest side will be m−n,

We know that , sum of two sides of a Δ is greater than 3rd side.

∴ m+m−n>m+n.

2m−n>m+n.

2m−m>n+n.

m>2n

or 2n<m

n< m/2.

I hope it helps.

Regards.

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If m-n , m , m+n are the lengths of the sides of an obtuse angled triangle , then n lies in

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Question : x, y, and z are the sides of a triangle. If z is the largest side and x²+ y² > z², then the triangle is a:
Option 1: Isosceles right angled triangle
Option 2: Acute angled triangle
Option 3: Obtuse angled triangle
Option 4: Right angled triangle

Question : If the sides of a triangle are in the ratio $3:1\frac{1}{4}:3\frac{1}{4}$, then the triangle is:
Option 1: Right-angled triangle
Option 2: Obtuse triangle
Option 3: Equiangular triangle
Option 4: Acute triangle

Question : The orthocentre of an obtuse-angled triangle lies:
Option 1: Inside the triangle
Option 2: Outside the triangle
Option 3: On one side of a triangle
Option 4: None of these

Question : Which of the following sets of lengths (in cm) will give three sides of an obtuse-angled triangle?
Option 1: 15, 62, 64
Option 2: 17, 64, 66
Option 3: 16, 63, 65
Option 4: 18, 65, 67