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?

Given :

The lengths of two sides of a triangle are 12 cm and 15 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 $= 12 + 15 = 27$

So, $27 > Third side$.

Difference between the two sides,

Case 1 :

$= 12 - 15 = -3$

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

Case 2 :

$15 - 12 = 3$

So, $Third side > 3$.

We can infer that, $27 > Third side > 3$.

Therefore, the third side of the triangle can be lie between 27 and 3.

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Updated on: 10-Oct-2022

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