SS1 Maths geometrical figure

2010-05-06 2:53 am

In the figure, the area of square ABCD is x cm^2 and CEFG is a rectangle.
The length CG of the rectangle is 1 cm longer than a side of the square.
The length CG of the rectangle is 1 cm longer than a side of the square.
The width FG of the rectangle is 0.5 shorter than a side of the square.

a) Express CG and FG is terms of x.

b) If the total area of ABCD and CEFG is 19 cm^2, find the area of ABCD

Figure: http://img140.imageshack.us/i/52330310.jpg/

更新1:

Ans: a) CG = ( x^ 0.5 +1 ) cm, FG= ( x^ 0.5 -0.5 ) cm b) 9 cm^ 2

回答 (1)

STEVIE-G™

2010-05-06 3:33 am

✔ 最佳答案

The figure cannot be shown....

2010-05-05 19:33:34 補充：
a)
The side of the square=x^0.5 cm
The length CG of the rectangle is 1 cm longer than a side of the square
CG=(x^0.5+1)cm
The width FG of the rectangle is 0.5 shorter than a side of the square
FG=(x^0.5-0.5)cm

b)
The area of CEFG
=CG*FG
=(x^0.5+1)(x^0.5-0.5)
=x-0.5x^0.5+x^0.5-0.5
=(x+0.5x^0.5-0.5)cm^2...(1)

If the total area of ABCD and CEFG is 19 cm^2,
then the area of CEFG
=19-the area of ABCD
=19-x...(2)

With the result of (1) and (2), we have
x+0.5x^0.5-0.5=19-x
2x+0.5x^0.5-19.5
4x+x^0.5-39=0
4(x^0.5)^2+x^0.5-39=0
(4x^0.5+13)(x^0.5-3)=0
x^0.5=-13/4 (rejected) or x^0.5=3
x=9

So, the required area=9cm^2

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