Question

1. examine the sets of numbers and decide which set are the sides of a triangle. select two correct answers.

a. 2 cm, 3 cm, 6 cm
b. 3 cm, 4 cm, 5 cm
c. 7 cm, 7 cm, 14 cm
d. 5 cm, 6 cm, 9 cm
e. 4.2 cm, 2.5 cm, 6.8 cm
□a
□b
□c
□d
□e

Explanation:

Step1: Recall triangle inequality rule

For sides $a,b,c$, $a+b>c$, $a+c>b$, $b+c>a$

Step2: Test Option A

$2+3=5 < 6$ → Fails rule

Step3: Test Option B

$3+4>5$, $3+5>4$, $4+5>3$ → Passes rule

Step4: Test Option C

$7+7=14$ → Fails rule

Step5: Test Option D

$5+6>9$, $5+9>6$, $6+9>5$ → Passes rule

Step6: Test Option E

$4.2+2.5=6.7 < 6.8$ → Fails rule

Answer:

B. 3 cm, 4 cm, 5 cm
D. 5 cm, 6 cm, 9 cm