Final answer:
Queen Hecuba and King Priam decide to kill their child due to the tragic events and circumstances of the Trojan War, as described in the play.
Step-by-step explanation:
According to the play, the reason why Queen Hecuba and King Priam decide to kill their child is due to the tragic events and circumstances that they find themselves in. In Greek mythology, the Trojan War led to the downfall of Troy, and the deaths of many of its citizens. In their despair and desperation, Hecuba and Priam make the difficult decision to sacrifice their child as a form of mercy, rather than subjecting them to the horrors of war and potential enslavement. This tragic act showcases the extreme emotional toll that the war has taken on the royal couple and adds to the overall tragic nature of the play.