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:
- \( AB + BC > AC \)
- \( AB + AC > BC \)
- \( AC + BC > AB \)
Applying these to our triangle:
-
\( 2,200 + 1,320 > AC \)
\( 3,520 > AC \) -
\( 2,200 + AC > 1,320 \)
\( AC > 1,320 - 2,200 \)
This results in \( AC > -880 \), which is irrelevant because distance cannot be negative. -
\( AC + 1,320 > 2,200 \)
\( AC > 2,200 - 1,320 \)
\( AC > 880 \)
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.