Question
Download Solution PDFIf in acute-angled triangle ABC, AL, BM, and CN are the three altitudes of triangle ABC, then which of the following statements will be true?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
AL, BM, and CN are the three altitudes of triangle ABC
Concept used
The side opposite to the greater angle is a greater
Calculation
In the above diagram,
∠ALB = 90
∠ABL < 90
Now side opposite to ∠ALB is AB and the side opposite to ∠ABL is AL
Since the side opposite to the greater angle is a greater
AB > AL ..(1)
Similarly in triangle BMC
BC > BM ..(2)
Similarly in triangle ANC
CA > CN ..(3)
Adding all three:
AL + BM + CN < AB + BC + CA
The answer is AL + BM + CN < AB + BC + CA
Last updated on Jul 14, 2025
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