If the three sides of a triangle are 12, 22 and m units, then which of the following is correct?

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SSC CPO 2024 Official Paper-I (Held On: 28 Jun, 2024 Shift 2)
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  1. 10 ≤ m < 34
  2. 10 ≤ m ≤ 34
  3. 10 < m < 34
  4. 10 < m ≤ 34

Answer (Detailed Solution Below)

Option 3 : 10 < m < 34
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SSC CPO : General Intelligence & Reasoning Sectional Test 1
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Detailed Solution

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Given:

The three sides of a triangle are 12, 22, and m units.

Formula Used:

For any triangle, the sum of any two sides must be greater than the third side and difference of two sides must be less than the third side.

Calculation:

We need to satisfy the triangle inequality theorem for all combinations:

1)  12 + 22 > m

⇒ 34 > m

⇒ m < 34

2) 12 + m > 22

⇒ m > 22 - 12

⇒ m > 10

Combining the inequalities from 1 and 2:

⇒ 10 < m < 34

The correct answer is option 3.

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