Question

determine if the given side lengths would create a triangle. choose yes or no:
a 3, 9, and 8
b 37, 13, and 21
c 16, 6, and 2
d 7, 5, and 10
yes, form a triangle. no, do not form a triangle.

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 side - lengths 3, 9, and 8:
$3 + 8=11>9$, $3 + 9 = 12>8$, $8 + 9=17>3$. So, it forms a triangle.

Step3: Check option B

For side - lengths 37, 13, and 21:
$13+21 = 34<37$. So, it does not form a triangle.

Step4: Check option C

For side - lengths 16, 6, and 2:
$6 + 2=8<16$. So, it does not form a triangle.

Step5: Check option D

For side - lengths 7, 5, and 10:
$5 + 7 = 12>10$, $5+10 = 15>7$, $7 + 10=17>5$. So, it forms a triangle.

Answer:

A. Yes, form a triangle.
B. No, do not form a triangle.
C. No, do not form a triangle.
D. Yes, form a triangle.