In which era did artists use the style of elongated proportions in exaggerated poses

Mannerism

Explanation:

Mannerism is a movement that arose during the Late Renaissance, around 1520, and lasted until the end of the 16th century in Italy (and the early 17th century in Northern countries). This style is recognizable due to its exaggeration of beauty and elegance, often resulting in figures that are asymmetrical. This was a reaction to the more harmonious ideals associated with the painters of the early Renaissance.

probably because the owner wants to get rid of it