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初中数学中有一类探求满足多个条件的动点问题。一般情况下,探求满足两个条件的动点问题时,我们先确定(或假设)一个条件满足,再通过计算、说理来确定另一个条件是否满足。例1如图1,在△ABC中,∠=90因,AC=6,BC=8,设直线l与斜边AB交于点E,与直角边交于点F,设AE=x,是否存在直线l同时平分△ABC的周长和面积?若存在直线l,求出x的值;若不存在直线l,请说明理由。解析:△ABC的周长为24,面积为24。先假设EF平分△ABC的周长,再通过解方程来
There is a class of mathematics in junior high school seeking to meet the multiple conditions of moving point problem. In general, when we explore the moving point problem that satisfies two conditions, we first determine (or assume) a condition is satisfied, and then we can determine whether another condition is satisfied through calculation and reasoning. Example 1 As shown in Figure 1, in △ ABC, ∠ = 90 due, AC = 6, BC = 8, set straight line l and hypotenuse AB at point E, intersect with right angle at point F, set AE = x, whether There is a straight line l while bisecting △ ABC perimeter and area? If there is a straight line l, find the value of x; if there is no straight line l, please explain the reasons. Analysis: △ ABC perimeter of 24, an area of 24. First assume that EF bisects the perimeter of ABC, then by solving the equation