Question

Given two sides of lengths 28 in. and 17 in., what are all possible lengths of a third side if you want to make a triangle?

a) 11 in.
b) 15 in.
c) 28 in.
d) 45 in.

Answer 1

The possible lengths of the third side of a triangle, given two sides of lengths 28 in. and 17 in., are lengths that are greater than 11 inches but less than 45 inches. Options (b) 15 in. and (c) 28 in. are the viable choices toward forming a triangle.

Step-by-step explanation:

To find all possible lengths of a third side of a triangle given two sides of lengths 28 in. and 17 in., we use the triangle inequality theorem. The theorem states that the length of any side of a triangle must be less than the sum and more than the difference of the lengths of the other two sides.

So, the possible length of the third side can be calculated using the following inequalities:

1. It must be greater than the difference of the other two side lengths: |28 - 17| = 11 in.
2. It must be less than the sum of the other two side lengths: 28 + 17 = 45 in.

Therefore, the length of the third side must be greater than 11 inches and less than 45 inches. Among the options provided (a) 11 in., (b) 15 in., (c) 28 in., (d) 45 in., the possible lengths are:

• 15 in.
• 28 in.

The other lengths, 11 in. and 45 in., do not satisfy the triangle inequality theorem since they represent the minimum and maximum limits, which are not included in the possible lengths.