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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?

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?

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Let ABC be a triangle with AB = 12cm and BC = 15cm

Now

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.

 

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