Which of these triangles are possible to construct by knowing only its altitude?a)Right angled triangleb)Equilateral trianglec)Isosceles triangled)Any triangleCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Because measure of the 3 angles are always equal in an equilateral triangle....

Answer

Equilateral triangles are possible to construct by knowing only its altitude . Because all the three angles and sides of an equilateral triangle are equal .

Answer

Understanding Triangle Construction with Altitude
When constructing triangles based solely on altitude, it is important to analyze the properties of different types of triangles.

Right Angled Triangle
- A right-angled triangle can have varying base lengths and side lengths for a given altitude.
- Knowing only the altitude does not uniquely determine the triangle, as multiple configurations can exist.

Equilateral Triangle
- An equilateral triangle has all sides equal and all angles equal (each measuring 60 degrees).
- The altitude from any vertex to the opposite side divides the triangle into two 30-60-90 triangles.
- The altitude uniquely determines the triangle's dimensions, allowing for accurate construction.

Isosceles Triangle
- An isosceles triangle has two equal sides and can have various configurations based on the altitude.
- Similar to right-angled triangles, knowing only the altitude does not uniquely define the triangle, as different bases can yield the same altitude.

Any Triangle
- A triangle with arbitrary side lengths can be constructed with given altitudes, but this is not unique.
- The altitude does not provide enough information to construct a triangle that is fixed in shape.

Conclusion
- Among the options, only the equilateral triangle can be uniquely constructed with just the knowledge of its altitude, making it the correct answer.
- The other types of triangles, including right-angled, isosceles, and any triangle, do not allow for unique reconstruction from altitude alone.

Answer

Eqilateral triangle

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