Question

The side lengths of possible triangles are listed in the table below. Choose from the Dropdown menu as to whether or not eachset could make a triangle.

Answer 1

When the length of sides of a triangle is given, the set of sides can make a triangle only if it follows the triangle inequality theorem.

The triangle inequality theorem states that the sum of any two sides of the triangle is greater than its third side.

Hence, from the above condition,

Part A

Length of sides 7,7,7 will make a triangle because the sum of any two sides (7+7)=14 is greater than the length of its third side (7)

(7+7) > 7

Therefore, 7,7,7 will make a triangle.

Part B

Length of sides 1,2,3 will not make a triangle because one combination of the sum of any two sides (1+2)=3 is not greater than the length of its third side (3). All combinations must satisfy the theorem

(1+2) = 3

(1+3) > 2

(2+3) > 1

Therefore, 1,2,3 will not make a triangle since one of it does not meet the condition

Part C

Length of sides 3.5,5,7 will make a triangle because the sum of any two sides (3.5+5)=8.5 is greater than the length of its third side (7)

(3.5+5) > 7

(3.5+7) > 5

(5+7) > 3.5

Therefore, 3.5,5,7 will make a triangle.