Question

(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 amandas (a) to chads (c)?
(1 point)
880 ft
1,040 ft
3,520 ft
4,400 ft

Explanation:

Step1: Apply triangle - inequality theorem

Let the distance from Amanda's to the baseball diamond \(AB = 2200\) ft and the distance from Chad's to the baseball diamond \(BC=1320\) ft. Let the distance from Amanda's to Chad's be \(AC = x\). According to the triangle - inequality theorem, \(|AB - BC|\leq x\leq AB + BC\).

Step2: Calculate the lower and upper bounds

First, calculate the lower - bound: \(|2200 - 1320|=880\) ft. Second, calculate the upper - bound: \(2200 + 1320 = 3520\) ft. So, \(880\leq x\leq3520\). But \(x
eq880\) and \(x
eq3520\) because the three points \(A\), \(B\), and \(C\) form a non - degenerate triangle. Among the given options, \(1040\) ft satisfies the inequality.

Answer:

1040 ft