题目

阅读理解 Whenever we turn on the TV or radio, read the newspapers, or surf the Internet, we'll be surrounded by the word “diet” everywhere. We have so easily been attracted by the promise of diet products that we have stopped thinking about what diet products are doing to us. We are paying for products that harm us psychologically and physically. It's obvious that diet products weaken us psychologically. They allow us to jump over the thinking stage that our weight problems lie not in actually losing the weight, but in controlling the consumption of fat. All we have to do is to swallow（2010•温州）如图，在Rt△ABC中，∠ACB=90°，AC=3，BC=4，过点B作射线BB1∥AC．动点D从点A出发沿射线AC方向以每秒5个单位的速度运动，同时动点E从点C出发沿射线AC方向以每秒3个单位的速度运动．过点D作DH⊥AB于H，过点E作EF上AC交射线BB1于F，G是EF中点，连接DG．设点D运动的时间为t秒．（1）当t为何值时，AD=AB，并求出此时DE的长度；（2）当△DEG与△ACB相似时，求t的值；（3）以DH所在直线为对称轴，线段AC经轴对称变换后的图形为A′C′．①当t＞时，连接C′C，设四边形ACC′A′的面积为S，求S关于t的函数关系式；②当线段A′C′与射线BB′，有公共点时，求t的取值范围（写出答案即可）．