Question

Consider triangles having integer sides such that no side is greater than 4 units. How many such triangles are possible?

Answer 1

Answer:

2

Step-by-step explanation:

Answer 2

Given :- Consider triangles having integer sides such that no side is greater than 4 units. How many such triangles are possible ?

Solution :-

we know that, in a ∆ ,

• Sum of any two sides is always greater than the third side .
• Difference between any two sides is less than the third side .

so, Possible ∆'s with integers sides such that no side is greater than 4 units are :-

1) Equaliteral ∆'s :-

• 1 1 , 1
• 2, 2, 2
• 3, 3, 3
• 4, 4, 4
• 4 ∆'s .

2) Isosceles ∆'s :-

• 1, 1, 2 => 1 + 1 = 2 => sum of two sides is not greater than the third side . so ∆ is not possible .
• 1, 1, 3 => 1 + 1 < 3 => Not possible .
• 1, 1, 4 => 1 + 1 < 4 => Not possible .
• 1, 2, 2
• 1, 3, 3
• 1, 4, 4
• 2, 2, 3
• 2, 2, 4 => 2 + 2 = 4 => Not possible .
• 2, 3, 3
• 2, 4, 4
• 3, 3, 4
• 3, 4, 4
• 8 ∆'s .

3) Scalene triangles :-

• 2, 3, 4 => As 2 + 3 > 4 , 3 + 4 > 2 , 2 + 4 > 3 .
• 1 ∆ .

therefore,

→ Total possible ∆'s are = 4 + 8 + 1 = 13 (Ans.)

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