Question

Which three lengths could be the lengths of the sides of a triangle?

11 cm, 6 cm, 17 cm
6 cm, 22 cm, 10 cm
8 cm, 15 cm, 22 cm
22 cm, 5 cm, 10 cm

Answer 1

Rule:
if a triangle has sides p,q,r, then all of the following must be true

p+q > r
p+r > q
q+r > p

if any of the above inequalities are false, then a triangle can't be formed

Answer 2

basically, if you can add up any two sides and the result is NOT larger than the third side, then a triangle is NOT possible

for example, choice A has 11 cm, 6 cm, 17 cm

11+6 = 17

but the result of the addition(17) is NOT larger than the other side (17)

so a triangle is NOT possible for choice A

Answer 3

choice B is the same

10+6 = 16 but it is not larger than 22

so choice B is also not possible

Answer 4

So would it be C?

Answer 5

yes because D is out too

5+10 = 15 but it's not larger than 22

Answer 6

8 cm, 15 cm, 22 cm

8+15 = 23 which is larger than 22
8+22 = 30 which is larger than 15
15+22 = 37 which is larger than 8

all three inequalities (shown above) hold true, so a triangle is possible

Answer 7

Thanks

Answer 8

np