Question

61 which set of numbers could represent the lengths of the sides of a triangle? a 9,16,20 b 8,11,19 c 3,4,8 d 11,5,6

Explanation:

Step1: Recall triangle inequality theorem

For side lengths $a,b,c$, the sum of any two sides must be greater than the third side: $a+b>c$, $a+c>b$, $b+c>a$.

Step2: Test Option A (9,16,20)

$9+16=25>20$, $9+20=29>16$, $16+20=36>9$. All conditions satisfied.

Step3: Test Option B (8,11,19)

$8+11=19$, which is not greater than 19. Fails the theorem.

Step4: Test Option C (3,4,8)

$3+4=7<8$. Fails the theorem.

Step5: Test Option D (11,5,6)

$5+6=11$, which is not greater than 11. Fails the theorem.

Answer:

A. 9,16,20