Question

A frame designer is making a triangular frame. She has two sides

of length 18 inches and 27 inches. What are the possible lengths
(in whole inches) for the third side?

Group of answer choices

x 45

9 < x < 45

Not Possible

Answer 1

The possible lengths for the third side of the triangular frame are 9 < x < 45.

Step-by-step explanation:

To find the possible lengths for the third side of a triangular frame, we can use 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.

So, in this case, the possible lengths for the third side must satisfy the following inequalities:

• 18 + 27 > x
• x + 18 > 27
• x + 27 > 18

By solving these inequalities, we find that the possible lengths for the third side (x) are:

9 < x < 45