If two sides of a triangle are 8 cm and 13 cm, then the length of the third side is between a cm and b cm. Find the values of a and b such that a is less than b.

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Solution

As we know that, sum of two sides of triangle is always greater than third side.Two sides of triangles are 8 cm and 13 cm.
Let third side is x cm.
So 8+13>x
or x<21.....(1)
and. 8+x>13x>5.....(2)
and 13+x>8
x>−5....(3)
combining equation 1, 2,3
We get,
x=6,7,8,9....19,20
So there are 16 possibility of third side.
So value of a and b will be 5 and 21.

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