Question

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. What are the possible values of x for this triangle?

a. 3x3 cm
b. 5 cm
c. 40 cm

Answer 1

The possible values of x can be determined using the triangle inequality theorem. Option b has possible values of x less than 10 cm, while option c has possible values of x less than 80 cm.

Step-by-step explanation:

The possible values of x for this triangle can be determined by considering the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's consider the options:

1. a. 3x3 cm: The sum of two sides would be 3x + 3 cm. In order for this to be greater than the third side, we need to have 3x + 3 > x, which simplifies to 3 > -2x. Dividing by -2, we get x < -3/2. Therefore, this option does not satisfy the triangle inequality.
2. b. 5 cm: The sum of two sides would be 5 + 5 cm. In order for this to be greater than the third side, we need to have 10 > x. Therefore, any value of x less than 10 cm would satisfy the triangle inequality.
3. c. 40 cm: The sum of two sides would be 40 + 40 cm. In order for this to be greater than the third side, we need to have 80 > x. Therefore, any value of x less than 80 cm would satisfy the triangle inequality.

So, the possible values of x for this triangle are any values less than 10 cm for option b, and any values less than 80 cm for option c.