Question

Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 1 ft, 2 ft, 5 ft B. 3 ft, 4 ft, 5 ft C. 3 ft, 4 ft, 7 ft D. 2 ft, 4 ft, 7 ft

Answer 1

B. 3 ft, 4 ft, 5 ft

Explanation:

The triangle inequality requires ...

a + b > c

for any sides a, b, c. It is convenient to use "a" and "b" as the shortest sides, because meeting the condition for those guarantees that the condition is met for other assignments of side lengths to letters.

Checking the offered segment lengths, we find ...

• A: 1+2 > 5 . . . . not true
• B: 3+4 > 5 . . . TRUE . . . . . . . this is your triangle
• C: 3+4 > 7 . . . . not true*
• D: 2+4 > 7 . . . . not true

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* Some authors define the triangle inequality as including the "or equal to" case: a + b ≥ c. A triangle that has a+b=c will look like a line segment--it has no area. That may be why other authors don't allow that case to be called a triangle. Choice C has a+b=c, so would also be a triangle according to some authors.