Question

Mia is building a fence to form a triangle shaped garden. She has built one side 24 ft. long and another side 15 ft. long. What length could Mia build the last side of the fence? Responses 7 ft 7 ft 8 ft 8 ft 10 ft 10 ft 9 ft

Answer 1

To determine the length of the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have two sides of lengths 24 ft and 15 ft. Let x be the length of the third side. Then, according to the triangle inequality theorem, we have:

24 + 15 > x

39 > x

and

15 + x > 24

x > 9

Combining these inequalities, we have:

9 < x < 39

Therefore, the length of the third side of the fence could be any value between 9 ft and 39 ft, but it cannot be exactly 7 ft, 8 ft, or 10 ft. Out of the given options, the closest value to the range is 9 ft.