Ask a New Question
Menu

Use the image to answer the 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.

3,520 ft.
3,520 ft.

880 ft.
880 ft.

4,400 ft.

1 answer

To find a possible distance from Amanda's house (A) to Chad's house (C), we can use the information provided.

We know:

  • Amanda walks 2,200 ft to the baseball diamond (point B).
  • Chad walks 1,320 ft to the baseball diamond (point B).

Let:

  • The distance from Amanda (A) to Chad (C) be \( AC \) (which we want to find).
  • The distance from Amanda to the baseball diamond (A to B) = \( c = 2,200 , \text{ft} \).
  • The distance from Chad to the baseball diamond (C to B) = \( a = 1,320 , \text{ft} \).

The distance \( AC \) can be calculated using the triangle inequality theorem, which states that in any triangle, the length of one side must be less than the sum and greater than the difference of the lengths of the other two sides:

  1. \( AB + BC > AC \)
  2. \( AB + AC > BC \)
  3. \( AC + BC > AB \)

Applying these to our triangle:

  1. \( 2,200 + 1,320 > AC \)
    \( 3,520 > AC \)

  2. \( 2,200 + AC > 1,320 \)
    \( AC > 1,320 - 2,200 \)
    This results in \( AC > -880 \), which is irrelevant because distance cannot be negative.

  3. \( AC + 1,320 > 2,200 \)
    \( AC > 2,200 - 1,320 \)
    \( AC > 880 \)

From the inequalities, we find that:

  • \( AC > 880 \)
  • \( AC < 3,520 \)

Thus, a possible distance from Amanda’s house (A) to Chad’s house (C) that fits this range would be any distance greater than 880 ft and less than 3,520 ft.

Among the provided options:

  • 1,040 ft. (valid)
  • 3,520 ft. (not valid)
  • 880 ft. (not valid)
  • 4,400 ft. (not valid)

The answer would be 1,040 ft.