Two sides of a triangle each have length 5. All of the following could be the length of the third side EXCEPT
a) 1
b) 3
c) 4
d) root 50 (approx 7.07)
e)10

Question

Two sides of a triangle each have length 5 All of the following
could be the length of the third side EXCEPT
a) 1
b) 3
c) 4
d) root 50 (approx 7 07)
e)10

Neha Sethi · Accepted Answer

Dear student
This question is about the triangle inequality , which states that in triangle with two sidesA and B , the third side must be greater than the absolute value of the difference between A and Band smaller than the sum of A and BApplying the triangle inequality  to this problem, we see that the third side must be greater than the absolute value of the difference between the othere two sides which is5-5=0 and smaller than the sum of the two  other sides, which is5+5=10
The only answer choice that  does not satisfy this range of possible values is  10 since the third side must be less than 10
Regards

Two sides of a triangle each have length 5. All of the following could be the length of the third side EXCEPT a) 1 b) 3 c) 4 d) root 50 (approx 7.07) e)10

Two sides of a triangle each have length 5. All of the following could be the length of the third side EXCEPT
a) 1
b) 3
c) 4
d) root 50 (approx 7.07)
e)10