The perimeter of a triangle with sides of integer values is equal to 13. How many such triangles are possible?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 3)
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  1. 5
  2. 8
  3. 7
  4. 6

Answer (Detailed Solution Below)

Option 1 : 5
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Detailed Solution

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Concept used:

If the perimeter of the triangle is "p"

Let Total possible triangles "t"

If p = even, then

t = p2/48

If p = odd, then

t = (p + 3)2/48

Calculation:

According to the question,

Total possible triangles = (13 + 3)2/48

⇒ 5.33 ≈ 5

∴ Total possible triangles are 5.

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