1. Three sides of a rectangular playground are to be surrounded by a 60m fence.The remaining side is the entrance of the playground.
△===> (左右兩邊是fence,上邊是fence,下邊是entrance)
a)Find the maximum area of the playground.
b)Find the dimensions of the rectangular playground if its area is a maximum.
maths functionsQ1
2007-10-09 10:16 am
回答 (1)
2007-10-09 6:05 pm
✔ 最佳答案
Let x=length of side oppsite the entrance,then (60-x)/2 = length of sides adjacent to entrance.
A.
Area
A(x)=x*(60-x)/2=30x-x^2/2
At A(x)=maximum,
A'(x)=30-x=0, or x=30
So the maximum area of the playground is A(30)=30*30-450=450.
B.
The dimensions of the playground is x=30 m (opposite side of entrance),
and (60-x)/2=15 m (adjacent to entrance).
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