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 a b c or d which one is it

4,400 ft.
4,400 ft.

1,040 ft.
1,040 ft.

880 ft.
880 ft.

3,520 ft.
3,520 ft.
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Answer 1

To determine the possible distance from Amanda's location (A) to Chad's location (C), we can refer to the triangle inequality theorem. In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Here, we know:

• Amanda walks from A to B (the baseball diamond) and the distance is \( c = 2,200 \) ft.
• Chad walks from C to B and the distance is \( a = 1,320 \) ft.
• The distance we want to find is \( b \) (the distance from A to C).

According to the triangle inequality:

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

Plugging the known values into the inequalities:

1. \( 1,320 + b > 2,200 \) → \( b > 2,200 - 1,320 \) → \( b > 880 \)
2. \( 1,320 + 2,200 > b \) → \( 3,520 > b \)
3. \( b + 2,200 > 1,320 \) (This will always be true since \( b \) is positive.)

This means that \( b \) must be greater than 880 ft and less than 3,520 ft:

So, the possible distance from Amanda's house to Chad's house \( (A \text{ to } C) \) is:

1,040 ft (b), which is a value between 880 ft and 3,520 ft.

Therefore, the answer is:

1,040 ft.