Question

Which set of three numbers could be the side lengths of a triangle?

A.2, 4, 8
B.3, 5, 7
C.2, 4, 6
D.3, 5, 9

Answer 1

B is the answer. The sum of two triangle legs should be more than the legth of the third.

Answer 2

For any triangle, the third side must be greater than difference of two sides and less than the sum.

Let the third side be x.

for 2, 4 x > 2, x < 6.
8 does not fit in, so 2,4, 8 can't form triangle

for 3, 5 x > 2, x < 8.
7 does fit in, so 3,5, 7 can form a triangle.

Testing the others in the same, doesn't form the sides of a triangle.

So only set B 3,5,7 could be the side lengths of a triangle.