The length of two sides of a triangle are $ 4 \mathrm{~cm} $ and $ 6 \mathrm{~cm} $. Between what two measurements should the length of the third side fall?

Given :

The lengths of two sides of a triangle are 4 cm and 6 cm.

To do :

We have to find between what two measures should the length of the third side fall.

Solution :

A triangle should satisfy the following conditions,

(i) Sum of any two sides should be greater than the third side.

(ii) Difference between any two sides should be less than the third side.

Sum of two sides $= 4 + 6 = 10\ cm$

So, $10\ cm > $ Third side.

Difference between the two sides,

Case 1 :

$= 4 - 6 = -2$

The length of the side should be positive, so neglect case 1.

Case 2 :

$6 - 4 = 2\ cm$

So, Third side $ > 2\ cm$.

We can infer that, $10\ cm > $ Third side $> 2\ cm$.

Therefore, the length of the third side of the triangle falls between 2 cm and 10 cm. 

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Updated on: 10-Oct-2022

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