If a translation maps ∠i onto ∠k, which of the following statements is true?

triangles hgi and jgk; point h is between points j and g on segment jg, and point i is between points g and k on segment gk.

segment hi = 2 segment jk
δghi ~ δgjk
segment gh = 2 segment gj
∠g ≅ ∠k

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.