To find the possible distance from Amanda's house (A) to Chad's house (C), we can use the information provided about the distances they each walk to the baseball diamond (B).
Amanda walks 2,200 ft to the baseball diamond (B), so we label the distance from A to B as \( c = 2,200 \) ft.
Chad walks 1,320 ft to the baseball diamond (B), so we label the distance from C to B as \( a = 1,320 \) ft.
We can consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we need to find the distance \( b \) between A and C while ensuring it satisfies the triangle inequality with sides \( a \) and \( c \):
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
Substituting \( a = 1,320 \) ft and \( c = 2,200 \) ft into these inequalities:
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\( 1,320 + b > 2,200 \) This simplifies to \( b > 2,200 - 1,320 \), thus \( b > 880 \).
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\( 1,320 + 2,200 > b \) This simplifies to \( 3,520 > b \), thus \( b < 3,520 \).
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\( b + 2,200 > 1,320 \) This is always true, as \( b + 2,200 > 1,320 \) gives no additional restrictions.
Combining the results from the inequalities involving \( b \), we have \( 880 < b < 3,520 \).
Now, let’s look at the possible distances provided:
- 3,520 ft.
- 1,040 ft.
- 880 ft.
- 4,400 ft.
Since \( b \) must be greater than 880 ft and less than 3,520 ft, the only option that fits these criteria is 1,040 ft.
Therefore, a possible distance from Amanda's (A) to Chad's (C) is 1,040 ft.
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