Question

Question #e9f9f

Answer 1

5, 9, and 10 will make a triangle due to the triangle inequality theorem holding true.

Explanation:

Recall the triangle inequality theorem, which states that the third side of a triangle is greater than the absolute value of the difference of the first two sides and less than the sum of the first two sides.

Let the first two sides be a and b, and the third side be c, so our inequality can be written as:

`abs(a-b)< c < a+b`

Try the first case:

`abs(5-9)< 10 < 5+9`

`=4<10<14`

This inequality holds true, so 5, 9, and 10 will make a triangle.

Try the second case:

`abs(2-3)< 5 < 2+3`

`=1<5<5`

This inequality does not hold true, so 2, 3, and 5 will not make a triangle.

Try the third case:

`abs(3-4) < 10 < 3+4`

`1 < 10 < 7`

This inequality does not hold true, so 3, 4, and 10 will not make a triangle.

Try the fourth case:

`abs(1-1)< 3 < 1+1`

`0 < 3 < 2`

This inequality does not hold true, so 1, 1, and 3 will not make a triangle.