Question

question 16 of 25
which set of three numbers could be the side lengths of a triangle?
a. 3, 5, 7
b. 2, 4, 6
c. 2, 4, 8
d. 3, 5, 9

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check option A

For 3, 5, 7:
$3 + 5=8>7$
$3 + 7 = 10>5$
$5 + 7=12>3$

Step3: Check option B

For 2, 4, 6:
$2+4 = 6$, which does not satisfy the triangle - inequality theorem since the sum of two sides is not greater than the third side.

Step4: Check option C

For 2, 4, 8:
$2 + 4=6<8$, which does not satisfy the triangle - inequality theorem.

Step5: Check option D

For 3, 5, 9:
$3+5 = 8<9$, which does not satisfy the triangle - inequality theorem.

Answer:

A. 3, 5, 7