Question

A triangle has two sides of lengths 4 and 7. What value could the length of the third side be

? check all that apply
A.3
B.5
C.7
D.9
E.11
F.17

Answer 1

B.5

C.7

D.9

Explanation:

a,b and c are the sides of a triangle if it satisfies:

a<b+c , b<a+c and c<b+a

Here, a=4 and b=7

We have to find c

i.e. all those c which satisfies:

4<7+c , 7<4+c and c<4+7=11

A.3 it is not true since it doesn't satisfies second inequality

B.5 it is true

C.7 it is true

D.9 it is true

E.11 This is clearly false, since it doesn't satisfies inequality third

F.17 This is clearly false, since it doesn't satisfies inequality third

Hence, correct options are:

B.5

C.7

D.9