题目内容

In the Rt△ABC，∠ACB=90°，AB+BC+CA=2+ $数学公式$ ，midline for hypotenuse（斜边）is 1，then AC?BC=________．

1
分析：根据告诉的斜边的中线的长为1，求得斜边的长，则两直角边的和等于 $\text{[math]}$ ，然后设出一直角边的长，利用勾股定理得到方程，将两直角边求出来，计算它们的积即可．
解答：∵斜边的中线的长为1，
∴斜边AB的长为2，
∴BC+CA=2+ $\text{[math]}$ -AB=2+ $\text{[math]}$ -2= $\text{[math]}$ ，
设BC的长为x，则AC的长为 $\text{[math]}$ -x，
根据勾股定理得： $\text{[math]}$
整理得： $\text{[math]}$
∵BC+CA= $\text{[math]}$ ，
∴AC?BC=1，
故答案为1．
点评：本题考查了勾股定理的相关知识，同时题目中还应用到了一元二次方程根与系数的关系，是一道不错的综合考题．

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In the Rt△ABC，∠ACB=90°，AB+BC+CA=2+，midline for hypotenuse（斜边）is 1，then AC?BC=________．

试题分类

In the Rt△ABC，∠ACB=90°，AB+BC+CA=2+ $数学公式$ ，midline for hypotenuse（斜边）is 1，then AC?BC=________．