题干

如图,某旅游景点要在长、宽分别为20米、12米的矩形水池的正中央建一个与矩形的边互相平行的正方形观赏亭,观赏亭的四边连接四条与矩形的边互相平行的且宽度相等的道路,已知道路的宽为正方形边长的
1
4
.若道路与观赏亭的面积之和是矩形水池面积的
1
6
,求道路的宽.
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答案(点此获取答案解析)

解:设道路的宽为x米,
则可列方程:
x(12﹣4x)+x(20﹣4x)+16x2=
1
6
×20×12,
即:x2+4x﹣5=0,
解得:x1=l,x2

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