Question : In a triangle, if three altitudes are equal, then the triangle is:
Option 1: obtuse
Option 2: equilateral
Option 3: right-angled
Option 4: Isosceles

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

Correct Answer: equilateral

Solution :
AD, BE and CF are the altitudes drawn on sides BC, CA and AB of $△$ ABC such that AD = BE = CF.
Since area of triangle = $\frac{1}{2}$ × base × corresponding altitude,
Area of $△$ ABC = $\frac{1}{2}$ × BC × AD = $\frac{1}{2}$ × AB × CF = $\frac{1}{2}$ × CA × BE
⇒ BC × AD = AB × CF = CA × BE
Since AD = BE = CF,
⇒ BC = AB = CA
⇒ $△$ ABC is an equilateral triangle.
Hence, the correct answer is equilateral.

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Question : In a triangle, if three altitudes are equal, then the triangle is:Option 1: obtuseOption 2: equilateralOption 3: right-angledOption 4: Isosceles

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Question : In a triangle, if three altitudes are equal, then the triangle is:
Option 1: obtuse
Option 2: equilateral
Option 3: right-angled
Option 4: Isosceles