Question

question 21 of 25
which set of three numbers could be the side lengths of a triangle?
a. 4, 10, 3
b. 4, 10, 6
c. 4, 7, 11
d. 4, 7, 7

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

$4 + 3=7<10$, so 4, 10, 3 cannot be side - lengths of a triangle.

Step3: Check option B

$4 + 6 = 10$, which does not satisfy the triangle - inequality theorem. So 4, 10, 6 cannot be side - lengths of a triangle.

Step4: Check option C

$4+7 = 11$, which does not satisfy the triangle - inequality theorem. So 4, 7, 11 cannot be side - lengths of a triangle.

Step5: Check option D

$4 + 7=11>7$, $4+7 = 11>7$, and $7 + 7=14>4$. So 4, 7, 7 can be side - lengths of a triangle.

Answer:

D. 4, 7, 7