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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 solve it and tell me the correct answer

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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1 answer

To find a possible distance from Amanda's house (A) to Chad's house (C), we can use the information about the distances Amanda and Chad walk to the baseball diamond (B).

  1. Amanda walks from A to B which is 2,200 ft.
  2. Chad walks from C to B which is 1,320 ft.

We are looking for the distance AC (from Amanda's house to Chad's house).

Let the distances be:

  • AB = c = 2200 ft (Amanda's distance)
  • CB = a = 1320 ft (Chad's distance)

Now, to find AC, we can use the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

In our case:

  • AC + CB > AB --> AC + 1320 > 2200
  • AC + AB > CB --> AC + 2200 > 1320
  • AB + CB > AC --> 2200 + 1320 > AC

From the first inequality: AC + 1320 > 2200 => AC > 880 ft

From the second inequality: AC + 2200 > 1320 => AC > -880 ft (This is always true.)

From the third inequality: 2200 + 1320 > AC => 3520 > AC (or AC < 3520 ft)

Putting this together, we have: 880 < AC < 3520

This means possible distances from A to C can be any value greater than 880 ft and less than 3520 ft.

Among the options given:

  • 4,400 ft: Not possible (it exceeds 3,520 ft)
  • 1,040 ft: Possible (it is greater than 880 ft)
  • 880 ft: Not possible (it cannot be equal to 880 ft)
  • 3,520 ft: Not possible (it cannot be equal to 3,520 ft)

Thus, the only feasible distance from Amanda's house to Chad's house in the options given is 1,040 ft.