Ex 6.4, 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?
In a triangle,
Sum of two sides > Third side
So,
12 + 8 > Third side
27 > Third side
⇒ Third side < 27
Also,
12 + Third side > 15
Third side > 15 − 12
Third side > 15 − 12
Third side > 3
Also,
15 + Third side > 12
Third side + 15 − 15 > 12 − 15
Third side > − 3
Since, third side will be positive.
So, this is always true
∴ We ignore this equation
So, our equations are
Third side > 3
Third side < 27
So,
Third side is greater than 3 cm
but less than 27 cm

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.