Use the image to answer the question.

Question

A triangle upper A upper B upper C. The edge upper A upper B is labeled c. The edge upper A upper C is labeled b. The edge upper B upper C is labeled a.

(Diagram is not to scale.)

In the diagram, Amanda lives at A
, Chad lives at C
, and B
represents the baseball diamond. Amanda tells Chad she walks 2,200 ft. to the baseball diamond. Chad says he only walks 1,320 ft., so she should come to his house and walk with him. What is a possible distance from Amanda’s (A)
to Chad’s (C)
?

(1 point)
Responses

1,040 ft.
1,040 ft.

880 ft.
880 ft.

4,400 ft.
4,400 ft.

3,520 ft.

Answer 1

To find a possible distance from Amanda's location (A) to Chad's location (C), we can utilize the triangle inequality theorem. This theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must hold true:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

In the given scenario:

• The distance from Amanda (A) to the baseball diamond (B) is \(c = 2200\) ft.
• The distance from Chad (C) to the baseball diamond (B) is \(a = 1320\) ft.
• We need to determine a possible distance \(b\) from Amanda (A) to Chad (C).

Using the triangle inequality:

1. \(2200 + b > 1320\)
   → \(b > 1320 - 2200\)
   → \(b > -880\) (This is always true since distance cannot be negative.)

2. \(1320 + b > 2200\)
   → \(b > 2200 - 1320\)
   → \(b > 880\)

3. \(2200 + 1320 > b\)
   → \(3520 > b\)
   → \(b < 3520\)

Now, combining these results, we find:

• \(b > 880\)
• \(b < 3520\)

This means the possible distance from Amanda’s house (A) to Chad’s house (C) can be any value greater than 880 ft and less than 3520 ft.

From the given response options:

• 1,040 ft (valid)
• 880 ft (not valid since it does not satisfy \(b > 880\))
• 4,400 ft (not valid since it exceeds \(3520\))
• 3,520 ft (not valid since it does not satisfy \(b < 3520\))

Thus, the possible distance from Amanda’s (A) to Chad’s (C) is 1,040 ft.