中四聯立方程問題..急問

設大正方邊長xcm,小正方邊長ycm,則

4x + 4y = 52.............(1)
x^2 + y^2 = 89..........(2)

由(1), x+y=13, x=13-y,代入(2) ;

(13-y)^2 + y^2 = 89

y^2-26y+169+y^2 = 89

2y^2 - 26y + 80=0

y^2-13y+40=0

(y-5)(y-8)=0

y=5 或 y=8(舍去),
x=8 或 x=5(舍去)

較小的 正方形報告板的大小 = 5*5=25cm2

2009-02-20 00:16:41 補充：
較小的 正方形報告板的邊長是5cm,週界是5*4=20cm

Let x be the length of one part of the string
and y be the length of remaining part of the string

x + y = 52 .........(1)
(x/4)^2 + (y/4)^2 = 89........(2)

from (1), x = 52-y
then put it into (2),
[(52-y)/4]^2 + (y/4)^2 = 89
(52-y)^2 + y^2 = 89*4^2
2704 - 104y + 2y^2 = 1424
y^2 - 52y + 640 = 0
(y-32)(y-20)=0
y=32 or 20

較小的正方形報告板的邊長是 20cm

2009-02-19 23:28:23 補充：
更正:

較小的正方形報告板的周界是 20cm, 面積是25cm^2