Question:medium
If the orthocenter, centroid, incenter and circumcentre coincide in a triangle $ABC$, and if the length of side $AB$ is $\sqrt{75}$ units, then the length of the altitude of the triangle through the vertex $A$ is:
If the orthocenter, centroid, incenter and circumcentre coincide in a triangle $ABC$, and if the length of side $AB$ is $\sqrt{75}$ units, then the length of the altitude of the triangle through the vertex $A$ is:
Show Hint
In any equilateral triangle with side $a$, the altitude, median, and perpendicular bisector are the same segment with length $a\sin(60^\circ)$. Always simplify square roots like $\sqrt{75}$ early to make the multiplication cleaner.
Updated On: May 2, 2026
- $\sqrt{3}$ units
- $3$ units
- $\frac{\sqrt{15}}{2}$ units
- $\frac{15}{2}$ units
- $\frac{\sqrt{5}}{2}$ units
Show Solution
The Correct Option is D
Solution and Explanation
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