length of two side of a triangle are 6 cm and 9cm write all the possible length of the third side
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its third side could be of any length greater than the sum of its two sides that is
6+9=15 more than 15
6+9=15 more than 15
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The length of any side of a triangle cannot exceed the sum of the lengths of the other two sides. (I am allowing three collinear points to be considered vertices of a degenerate triangle.) Therefore, if two sides have length 6 cm and 9 cm, the third side has length between 9–6 = 3 cm and 9+6 = 15 cm. On the other hand, if we take a line segment whose length is any real number between 3 and 15 cm and construct a circle of radius 6 cm with center at one end and another circle of radius 15 cm with center at the other end, the two circles will intersect and a point of intersection will be the third vertex of a triangle with base the given line segment and whose two other sides are of length 6 cm and 9 cm. So the third side can be of any length between 3 and 15 cm.
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