Ask a New Question
Menu

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)

4,400 ft.

O 880 ft.

O 1,040 ft

O 3,520 ft

1 answer

To solve this problem, we can start by defining the distances involved.

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

We can apply the triangle inequality theorem here, which states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let \( D \) represent the distance from Amanda's house (A) to Chad's house (C). We have:

  • Distance from A to B: 2,200 ft
  • Distance from B to C: 1,320 ft

Using the triangle inequality:

  1. \( A + B > C \) would be \( 2,200 + 1,320 > D \)
  2. \( A + C > B \) would be \( D + 1,320 > 2,200 \)
  3. \( B + C > A \) would be \( 2,200 + D > 1,320 \)

From the second inequality:

  • \( D + 1,320 > 2,200 \)
  • \( D > 2,200 - 1,320 \)
  • \( D > 880 \)

From the first inequality:

  • \( 2,200 + 1,320 > D \)
  • \( D < 3,520 \)

So we have established that \( 880 < D < 3,520 \).

Now, looking at the given options, the possible distances are:

  • 4,400 ft (out of range)
  • 880 ft (not greater than 880)
  • 1,040 ft (within range)
  • 3,520 ft (not less than 3,520)

The only valid choice for the distance from Amanda's (A) to Chad's (C) is:

1,040 ft.