Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 3 ft, 6 ft, 9 ft B. 3 ft, 5 ft, 7 ft C. 3 ft, 6 ft, 12 ft D. 3 ft, 9 ft, 27 ft

Question

10-05-2018
Mathematics

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Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 3 ft, 6 ft, 9 ft B. 3 ft, 5 ft, 7 ft C. 3 ft, 6 ft, 12 ft D. 3 ft, 9 ft, 27 ft

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Louli Louli · Answer 1 · 2018-05-20T12:13:59+02:00

Answer:
B. 3 ft, 5 ft and 7 ft

Explanation:
In any triangle, the sum of any two sides must be greater that the third one.

Therefore, to know if the given sides represent a triangle or not, all what we will do is add the two short sides and compare the result to the largest one.
We would have 3 options:
sum of short sides > longest side ......> It is a triangle
sum of short sides < longest side ......> It is not a triangle
sum of short sides = longest sides ....> It is not a triangle

Now, for the given:
1- Option A:
sum of short sides = 3 + 6 = 9 ft which is equal to the longest side
This option is incorrect

2- Option B:
sum of short sides = 3 + 5 = 8 ft which is greater than the longest side
This option is correct

3- Option C:
sum of short sides = 3 + 6 = 9 ft which is less than the longest side
This option is incorrect

4- Option D:
sum of short sides = 3 + 9 = 12 ft which is less than the longest side
This option is incorrect

Based on the above, the only correct option is B.

Hope this helps :)