Question

A triangle has sides of length 4, 7, and x. Which of the following could be the value of x?

1) 2.9
2) 4.5
3) 6.25
4) 7
5) 12

Answer 1

The possible values of side x that could form a valid triangle with the other sides of lengths 4 and 7, according to the triangle inequality theorem, are 4.5, 6.25, and 7.

Step-by-step explanation:

The question involves finding the possible value of a side x in a triangle where the other two sides have lengths of 4 and 7. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Thus, for the given triangle:

1. x + 4 > 7
2. x + 7 > 4
3. 4 + 7 > x

We can simplify these inequalities to:

1. x > 3
2. x > -3
3. x < 11

Considering the options given, the value of x could be 2.9, 4.5, 6.25, 7, or 12. If we apply the triangle inequality theorem, we find that 2.9 does not satisfy the first inequality (x must be greater than 3). Therefore, options 2 (4.5), 3 (6.25) and 4 (7) are possible values for x, as they satisfy all three inequalities. However, 12 does not satisfy the third inequality (x must be less than 11), making it an impossible value for x. Hence, the values of x that could create a valid triangle in this case are 4.5, 6.25, and 7.