The number of possible triangles with any three of the lengths 1.2cm 4.2cm 5.9cm and 8.1cm is
Answers
Answer: One
Step-by-step explanation:
The key point required to solve this question is the fact that :
"Sum of any two sides of a triangle is always greater than the third side."
Now let us consider this fact and solve this question .
Let us find the sum all possible combinations of any two sides at a time.
i) 1.2 + 4.2 = 5.4 < 5.9 < 8.1
No triangle is possible with this combination.
ii) 1.2 + 5.9 = 7.1 < 8.1
This combination cannot form triangle with side 8.1 . Hence the only remaining option is 4.2
But in case one we have seen that no triangle with sides 4.2 and 1.2 is possible.
iii) 4.2 + 5.9 = 10.1
Hence this can make form a triangle with the other side as 8.1. Since the other side cannot be 1.2.
Therefore the only possible combination of triangle is with sides 4.2 cm ,5.9 cm ,8.1 cm.
Hope this helps
Number of possible triangles with any three of the lengths 1.2cm 4.2cm 5.9cm and 8.1cm is 1 (One)
Step-by-step explanation:
the number of possible triangles with any three of the lengths 1.2cm 4.2cm 5.9cm and 8.1cm
A triangle has three Sides
3 Sides out of 4 can be selected in ⁴C₃ = 4 Ways
and Combination must satisfy that sum of two sides > third side
Possible Combination
1.2 4.2 5.9 1.2 + 4.2 < 5.9 (Triangle not possible)
1.2 4.2 8.1 1.2 + 4.2 < 8.1 (Triangle not possible)
1.2 5.9 8.1 1.2 + 5.9 < 8.1 (Triangle not possible)
4.2 5.9 8.1 only Possible Triangle
only one triangle possible
Number of possible triangles with any three of the lengths 1.2cm 4.2cm 5.9cm and 8.1cm is 1 (One)
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