单选题
The figure above shows a rectangular play area in which one child stands at B while another child runs back and forth along the entire side AD．If the running child is in a position randomly located along side AD at a given time，what is the probability that the two children are at most 50 feet apart at that time?
The figure above shows a rectangular play area in which one child stands at B while another child runs back and forth along the entire side AD．If the running child is in a position randomly located along side AD at a given time，what is the probability that the two children are at most 50 feet apart at that time?
【正确答案】
D
【答案解析】左面图形表示一个长方形的娱乐区，有一个小孩站在B点，同时另一个小孩在A和D之问来回跑动。若跑步的小孩在AD边上的位置在任一时刻都是随机的，两个小孩最多相距50英尺的概率(probability)是多少?
根据题意可知，两个孩子的位置及点A在任意时刻都可构成一个直角三角形，直角三角形的斜边长就是两个孩子之间的距离，两个孩子的距离不超过50英尺，即直角三角形的斜边不超过50英尺，AB=30英尺，根据勾股定理可知，跑步的小孩离A点的距离应不超过40英尺时，才能使他们之间的距离不超过50英尺。而跑步的小孩在AD上的位置是随机的，因此两个小孩最多相距50英尺的概率是[*][*]
根据题意可知，两个孩子的位置及点A在任意时刻都可构成一个直角三角形，直角三角形的斜边长就是两个孩子之间的距离，两个孩子的距离不超过50英尺，即直角三角形的斜边不超过50英尺，AB=30英尺，根据勾股定理可知，跑步的小孩离A点的距离应不超过40英尺时，才能使他们之间的距离不超过50英尺。而跑步的小孩在AD上的位置是随机的，因此两个小孩最多相距50英尺的概率是[*][*]