Which of the following cannot be the sides of a triangle? (i) 4.5 cm, 3.5 cm, 6.4 cm (ii) 2.5 cm, 3.5 cm, 6.0 cm (iii) 2.5 cm, 4.2 cm, 8 cm
Answers
Answer:
Condition:
Sum of two sides should be greater than the third side.
i) 4.5 + 3.5 = 8 > 6.5
3.5 + 6.4 = 9.9 > 4.5
4.5 + 6.4 = 10.9 > 3.5
The sum of two sides is greater than the third side. So, they can form a triangle.
ii) 2.5 + 3.5 = 6 = 6
The sum of the two sides is equal to the sum of third side. So, it cannot form a triangle.
iii) 2.5 + 4.2 = 6.7 < 8
The sum of the two sides is lesser than the third side. So, it also cannot form a triangle.
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Solution :-
We know that, In any ∆ we have,
- Sum of any two sides of a ∆ is always greater than the third side .
- Difference between any two sides of a ∆ is always smaller than the third side .
So, checking all given options we get,
(i) 4.5 cm, 3.5 cm, 6.4 cm
→ 4.5 + 3.5 > 6.4 => 8 > 6.4
→ 3.5 + 6.4 > 4.5 => 9.9 > 4.5
→ 4.5 + 6.4 > 3.5 => 10.9 > 3.5
and,
→ 4.5 - 3.5 < 6.4 => 1 < 6.4
→ 6.4 - 3.5 < 4.5 => 2.9 < 4.5
→ 6.4 - 4.5 < 3.5 => 1.9 < 3.5
therefore, the given sides are possible .
(ii) 2.5 cm, 3.5 cm, 6.0 cm
→ 2.5 + 3.5 > 6.0 => 6 = 6
also,
→ 6.5 - 3.5 < 2.5 => 2.5 = 2.5
since sum of first two sides is not greater than third side and difference between third and first side is not smaller than second side but it is equal to third side . Therefore, triangle with sides is not possible .
(iii) 2.5 cm, 4.2 cm, 8 cm
→ 2.5 + 4.2 > 8
but,
→ 6.7 < 8 .
since sum of first two sides is smaller than the third side . Therefore, the given sides are not possible .
Hence, we can conclude that, Option (ii) and (iii) cannot be the sides of a triangle .
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