6. The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?
Let ABC be a triangle with AB = 12cm and BC = 15cm
As we know that the sum of two sides of ANY triangle is always greater than the third side(Triangles Inequality Rule).
AB + BC > CA
12 + 15 > CA
CA < 27......(1)
Also, in a similar way
AB + CA > BC
CA > BC - AB
CA > 15 - 12
CA > 3............(2)
Hence from (1) and (2), we can say that the length of third side of the triangle must be between 3cm to 27 cm.