Question

Which of the following sides can form the triangle ?

• A. AB= 5 m, BC = 4 m, AC =9 m
• B. AB= 5 m, BC = 4 m, AC =8 m
• C. AB= 5 m, BC = 4 m, AC = 12 m
• D. AB= 5 m, BC = 4 m, AC =14 m

Answer 1

The correct option is B AB= 5 m, BC = 4 m, AC =8 m

We have the theorem which states that " The sum of any two sides of a triangle is greater than the third side "

Consider the sides with lengths :

AB= 5 m, BC = 4 m, AC = 8 m
Considering sides AB and BC, we have
Sum of the sides AB and BC = 9 m
Third side AC = 8 m
We see that AB + BC > AC

Considering sides AB and AC, we have
Sum of the sides AB and AC = 13 m
Third side BC = 4 m
We see that AB + AC > BC

Considering sides AC and BC, we have
Sum of the sides AC and BC = 12 m
Third side AB = 5 m
We see that AC + BC > AB

So, the sides -AB= 5 m, BC = 4 m, AC = 8 m can form the triangle.

Consider the sides with lengths :
AB= 5 m, BC = 4 m, AC = 9 m
Sum of the sides AB and BC = 9 m
Third side AC = 9 m
We see that AB + BC = AC
Sum of two sides is not greater than the third side.
Therefore, these cannot be the sides of a triangle.

Consider the sides with lengths :
AB= 5 m, BC = 4 m, AC = 12 m
Sum of the sides AB and BC = 9 m
Third side AC = 12 m
We see that AB + BC < AC
Sum of two sides is not greater than the third side.
Therefore, these cannot be the sides of a triangle.

Consider the sides with lengths :
AB= 5 m, BC = 4 m, AC = 14 m
Sum of the sides AB and BC = 9 m
Third side AC = 14 m
We see that AB + BC < AC
Sum of two sides is not greater than the third side.
Therefore, these cannot be the sides of a triangle.