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Q.3 Show that the sum of three altitude of a triangle is less than the sum of the three sides of the triangle.?
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Q.3 Show that the sum of three altitude of a triangle is less than the...
The statement you have provided does not hold true for all triangles. In fact, it is not possible for the sum of the altitudes of a triangle to be less than the sum of its sides.
In order for a triangle to exist, it must satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides of lengths a, b, and c, the following inequality must hold:
a + b > c
b + c > a
c + a > b
Therefore, it is not possible for the sum of the three sides of a triangle to be less than the sum of its three altitudes.
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Q.3 Show that the sum of three altitude of a triangle is less than the sum of the three sides of the triangle.?
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