Question

*Which of the following triangles has its altitude exterior region of it?*
1️⃣ Right angle triangle
2️⃣ Equilateral triangle
3️⃣ Scalene triangle
4️⃣ Acute angled triangle​

Answer 1

Answer:

3️⃣ Scalene triangle

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Answer 2

Given :  Triangles  

1️⃣ Right angle triangle

2️⃣ Equilateral triangle

3️⃣ Scalene triangle

4️⃣ Acute angled triangle​

To Find : Which of these  triangles has its altitude in exterior region of it

Solution:

Altitudes are perpendicular drawn from the vertex on the opposite side of triangle

Obtuse angled triangle which has one angle greater than right angle has  altitude in exterior region of it

1️⃣ Right angle triangle  : ( one angle is right angles)

 Has two altitudes on intersection of perpendicular legs intersection and one on the hypotenuse

2️⃣ Equilateral triangle  ( all angles and side are equal )

Has all altitude at mid point of opposite sides

3️⃣ Scalene triangle All sides and angles are of unequal measures

Scalene triangle can be right angle , acute angled or obtuse angles triangle

So Scalene triangle which are obtuse  have its altitude in exterior region of it

Hence Scalene triangle can have its altitude in exterior region of it but not all the scalene triangles

4️⃣ Acute angled triangle​ - has all angles less than right angles

Altitudes are inside the triangle

Obtuse angled triangle has  altitude in exterior region of it

But From the given options Scalene triangle can be the answer as only scalene triangle can be obtuse triangle in the given option.

Option 3 is correct.

Note : All Scalene triangle Does not have altitude in the exterior region.

Also note that all obtuse angled triangle are not scalene they can be isosceles also.

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