Question

Which side lengths can represent the sides of a triangle?

Answer 1

Answer:

Option A $\sqrt{3},5,6$

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify each case

case A) we have

$\sqrt{3},5,6$

we know that

$\sqrt{3}=1.73$

Applying the Triangle Inequality Theorem

1) 5+6 > 1.73 -----> is true

2) 5+1.73 > 6 ----> is true

therefore

The side lengths can represent the sides of a triangle

case B) we have

$\sqrt{2},3,5$

we know that

$\sqrt{2}=1.41$

Applying the Triangle Inequality Theorem

1) 1.41+3 > 5 -----> is not true

therefore

The side lengths can not represent the sides of a triangle

case C) we have

$1,2,3$

Applying the Triangle Inequality Theorem

1) 1+2 > 3 ----> is not true

therefore

The side lengths can not represent the sides of a triangle

case D) we have

$2,5,8$

Applying the Triangle Inequality Theorem

1) 2+5 > 8 ----> is not true

therefore

The side lengths can not represent the sides of a triangle

Answer 2

Answer:

The solution is  

 square root 3

, 5, 6. To determine whether side lengths can form a triangle, we must check to make sure that the sum of any two sides is greater than the length of the third side. This is true with  

3 , 5, and 6.

Step-by-step explanation: