數......趕要!!! 4條....(20)

2008-10-04 6:29 am

1.The figure shows a piece of land in the shape of two adjacent squares.If the total area of the piece of land is 500cm^2 and its perimeter is 100m,

a)find two equations connecting x nd y,

b)hence find the length of the longest side of the piece of land.

2.the external perimeter of the rectangular field ABCD is38m and the overall area is 90m^2.

a)Express the perimeter and area of the rectangular field ABCD in terms of x and y.

b)Hence find the length of the diagonal BD correct to 2 decimal places.

回答 (1)

Train

2008-10-07 7:24 am

✔ 最佳答案

1a) Let x and y be the length of the two squares and y>x.
Total area of land:
x^2+y^2=500
Perimeter of land:
3x+(y-x)+3y=100
2x+4y=100
x+2y=50 or x=50-2y

1b) x^2+y^2=500
(50-2y)^2+y^2=500
2500-200y+4y^2+y^2=500
5y^2-200y+2000=0
y^2-40y+400=0
(y-20)^2=0
y-20=0
y=20
therefore, the length of the longest side of the piece of land is 20m.

2a)
Area of rectangle:
xy=90
Perimeter of rectangle:
2x+2y=38

2b)
Length of diagonal BD
√(x^2+y^2)
=√(x^2+y^2+2xy-2xy)
=√[(x+y)^2-2xy]
=√[19^2-2(90)]
=√(361-180)
=√181
=13.45m

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