Question

Can the side lengths of 2 9 12 form a triangle yes or no can the side lengths of 3 5 8 form a triangle yes or no can the side lengths of 10 12 15 form a triangle yes or no can the side length of 4 4 7 form a triangle yes or no

Answer 1

2,9 , 12

NO

3,5,8

No

10,12 , 15

Yes

4,4,7

Yes

Explanation:

Here, we want to know if the set of given sides will form a triangle

Mathematically, for a triangle to be formed, the sum of two sides must be greater than the third side

If we have a, b and c as sides of a triangle, then mathematically (

a + b > c

a + c > b

and b + c > a

If at any point, these does not work, then we can’t have a triangle

Let us consider the lengths one after the other

We proceed as follows;

2 9 12

Since 2 + 9 is not greater than 12, we cannot have a triangle

3 , 5, 8

Since 3 + 5 equals 8 and not greater than it, we cannot have a triangle

10 , 12 , 15

This forms a triangle

10 + 12 > 15

10 + 15 > 12

12 + 15 > 10

Lastly;

4 , 4 , 7

Since ;

4 + 4 > 7

and

4 + 7 > 4

we have a triangle