F.5 MATHS (不等式)......

2010-09-21 2:12 am

1.A gardener is going to put up 84m of fence around a rectangular plot of land.
If the area to be enclosed is at least 425m2, find the maximum length of the plot.

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回答 (1)

wkho28

2010-09-21 8:46 am

✔ 最佳答案

1. A gardener is going to put up 84 m of fence around a rectangular plot of land. If the area to be enclosed is at least 425 m^2, find the maximum length of the plot.

Let the length of the plot be x cm.
The width of the plot is :
(84-2x)/2 m = (42-x) m

The area to be enclosed is :
x(42-x) m^2

x(42-x)>425
x^2-42x+425<0
(x-17)(x-25)<0

case (i) :
(x-17)<0 and (x-25)>0
x<17 and x>25
No solution

case (ii) :
(x-17)>0 and (x-25)<0
x>17 and x<25
17<x<25

∴ The maximum length of the plot is 25 m.

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